# The importance of being open

Barcelona refused to stay indoors this May.

Merchandise spilled outside shops onto the streets, restaurateurs parked diners under trees, and ice-cream cones begged to be eaten on park benches. People thronged the streets, markets filled public squares, and the scents of flowers wafted from vendors’ stalls. I couldn’t blame the city. Its sunshine could have drawn Merlin out of his crystal cave. Insofar as a city lives, Barcelona epitomized a quotation by thermodynamicist Ilya Prigogine: “The main character of any living system is openness.”

Prigogine (1917–2003), who won the Nobel Prize for chemistry, had brought me to Barcelona. I was honored to receive, at the Joint European Thermodynamics Conference (JETC) there, the Ilya Prigogine Prize for a thermodynamics PhD thesis. The JETC convenes and awards the prize biennially; the last conference had taken place in Budapest. Barcelona suited the legacy of a thermodynamicist who illuminated open systems.

The conference center. Not bad, eh?

Ilya Prigogine began his life in Russia, grew up partially in Germany, settled in Brussels, and worked at American universities. His nobelprize.org biography reveals a mind open to many influences and disciplines: Before entering university, his “interest was more focused on history and archaeology, not to mention music, especially piano.” Yet Prigogine pursued chemistry.

He helped extend thermodynamics outside equilibrium. Thermodynamics is the study of energy, order, and time’s arrow in terms of large-scale properties, such as temperature, pressure, and volume. Many physicists think that thermodynamics describes only equilibrium. Equilibrium is a state of matter in which (1) large-scale properties remain mostly constant and (2) stuff (matter, energy, electric charge, etc.) doesn’t flow in any particular direction much. Apple pies reach equilibrium upon cooling on a countertop. When I’ve described my research as involving nonequilibrium thermodynamics, some colleagues have asked whether I’ve used an oxymoron. But “nonequilibrium thermodynamics” appears in Prigogine’s Nobel Lecture.

Ilya Prigogine

Another Nobel laureate, Lars Onsager, helped extend thermodynamics a little outside equilibrium. He imagined poking a system gently, as by putting a pie on a lukewarm stovetop or a magnet in a weak magnetic field. (Experts: Onsager studied the linear-response regime.) You can read about his work in my blog post “Long live Yale’s cemetery.” Systems poked slightly out of equilibrium tend to return to equilibrium: Equilibrium is stable. Systems flung far from equilibrium, as Prigogine showed, can behave differently.

A system can stay far from equilibrium by interacting with other systems. Imagine placing an apple pie atop a blistering stove. Heat will flow from the stove through the pie into the air. The pie will stay out of equilibrium due to interactions with what we call a “hot reservoir” (the stove) and a “cold reservoir” (the air). Systems (like pies) that interact with other systems (like stoves and air), we call “open.”

You and I are open: We inhale air, ingest food and drink, expel waste, and radiate heat. Matter and energy flow through us; we remain far from equilibrium. A bumper sticker in my high-school chemistry classroom encapsulated our status: “Old chemists don’t die. They come to equilibrium.” We remain far from equilibrium—alive—because our environment provides food and absorbs heat. If I’m an apple pie, the yogurt that I ate at breakfast serves as my stovetop, and the living room in which I breakfasted serves as the air above the stove. We live because of our interactions with our environments, because we’re open. Hence Prigogine’s claim, “The main character of any living system is openness.”

The author

JETC 2019 fostered openness. The conference sessions spanned length scales and mass scales, from quantum thermodynamics to biophysics to gravitation. One could arrive as an expert in cell membranes and learn about astrophysics.

I remain grateful for the prize-selection committee’s openness. The topics of earlier winning theses include desalination, colloidal suspensions, and falling liquid films. If you tipped those topics into a tube, swirled them around, and capped the tube with a kaleidoscope glass, you might glimpse my thesis’s topic, quantum steampunk. Also, of the nine foregoing Prigogine Prize winners, only one had earned his PhD in the US. I’m grateful for the JETC’s consideration of something completely different.

When Prigogine said, “openness,” he referred to exchanges of energy and mass. Humans can exhibit openness also to ideas. The JETC honored Prigogine’s legacy in more ways than one. Here’s hoping I live up to their example.

# Thermodynamics of quantum channels

You would hardly think that a quantum channel could have any sort of thermodynamic behavior. We were surprised, too.

How do the laws of thermodynamics apply in the quantum regime? Thanks to novel ideas introduced in the context of quantum information, scientists have been able to develop new ways to characterize the thermodynamic behavior of quantum states. If you’re a Quantum Frontiers regular, you have certainly read about these advances in Nicole’s captivating posts on the subject.

Asking the same question for quantum channels, however, turned out to be more challenging than expected. A quantum channel is a way of representing how an input state can change into an output state according to the laws of quantum mechanics. Let’s picture it as a box with an input state and an output state, like so:

A computing gate, the building block of quantum computers, is described by a quantum channel. Or, if Alice sends a photon to Bob over an optical fiber, then the whole process is represented by a quantum channel. Thus, by studying quantum channels directly we can derive statements that are valid regardless of the physical platform used to store and process the quantum information—ion traps, superconducting qubits, photonic qubits, NV centers, etc.

We asked the following question: If I’m given a quantum channel, can I transform it into another, different channel by using something like a miniature heat engine? If so, how much work do I need to spend in order to accomplish this task? The answer is tricky because of a few aspects in which quantum channels are more complicated than quantum states.

In this post, I’ll try to give some intuition behind our results, which were developed with the help of Mario Berta and Fernando Brandão, and which were recently published in Physical Review Letters.

First things first, let’s worry about how to study the thermodynamic behavior of miniature systems.

## Thermodynamics of small stuff

One of the important ideas that quantum information brought to thermodynamics is the idea of a resource theory. In a resource theory, we declare that there are certain kinds of states that are available for free, and that there are a set of operations that can be carried out for free. In a resource theory of thermodynamics, when we say “for free,” we mean “without expending any thermodynamic work.”

Here, the free states are those in thermal equilibrium at a fixed given temperature, and the free operations are those quantum operations that preserve energy and that introduce no noise into the system (we call those unitary operations). Faced with a task such as transforming one quantum state into another, we may ask whether or not it is possible to do so using the freely available operations. If that is not possible, we may then ask how much thermodynamic work we need to invest, in the form of additional energy at the input, in order to make the transformation possible.

Interestingly, the amount of work needed to go from one state ρ to another state σ might be unrelated to the work required to go back from σ to ρ. Indeed, the freely allowed operations can’t always be reversed; the reverse process usually requires a different sequence of operations, incurring an overhead. There is a mathematical framework to understand these transformations and this reversibility gap, in which generalized entropy measures play a central role. To avoid going down that road, let’s instead consider the macroscopic case in which we have a large number n of independent particles that are all in the same state ρ, a state which we denote by . Then something magical happens: This macroscopic state can be reversibly converted to and from another macroscopic state , where all particles are in some other state σ. That is, the work invested in the transformation from to can be entirely recovered by performing the reverse transformation:

If this rings a bell, that is because this is precisely the kind of thermodynamics that you will find in your favorite textbook. There is an optimal, reversible way of transforming any two thermodynamic states into each other, and the optimal work cost of the transformation is the difference of a corresponding quantity known as the thermodynamic potential. Here, the thermodynamic potential is a quantity known as the free energy . Therefore, the optimal work cost per copy w of transforming into is given by the difference in free energy .

## From quantum states to quantum channels

Can we repeat the same story for quantum channels? Suppose that we’re given a channel , which we picture as above as a box that transforms an input state into an output state. Using the freely available thermodynamic operations, can we “transform” into another channel ? That is, can we wrap this box with some kind of procedure that uses free thermodynamic operations to pre-process the input and post-process the output, such that the overall new process corresponds (approximately) to the quantum channel ? We might picture the situation like this:

Let us first simplify the question by supposing we don’t have a channel to start off with. How can we implement the channel from scratch, using only free thermodynamic operations and some invested work? That simple question led to pages and pages of calculations, lots of coffee, a few sleepless nights, and then more coffee. After finally overcoming several technical obstacles, we found that in the macroscopic limit of many copies of the channel, the corresponding amount of work per copy is given by the maximum difference of free energy F between the input and output of the channel. We decided to call this quantity the thermodynamic capacity of the channel:

Intuitively, an implementation of must be prepared to expend an amount of work corresponding to the worst possible transformation of an input state to its corresponding output state. It’s kind of obvious in retrospect. However, what is nontrivial is that one can find a single implementation that works for all input states.

It turned out that this quantity had already been studied before. An earlier paper by Navascués and García-Pintos had shown that it was exactly this quantity that characterized the amount of work per copy that could be extracted by “consuming” many copies of a process provided as black boxes.

To our surprise, we realized that Navascués and García-Pintos’s result implied that the transformation of into is reversible. There is a simple procedure to convert into at a cost per copy that equals . The procedure consists in first extracting work per copy of the first set of channels, and then preparing from scratch at a work cost of per copy:

Clearly, the reverse transformation yields back all the work invested in the forward transformation, making the transformation reversible. That’s because we could have started with ’s and finished with ’s instead of the opposite, and the associated work cost per copy would be . Thus the transformation is, indeed, reversible:

In turn, this implies that in the many-copy regime, quantum channels have a macroscopic thermodynamic behavior. That is, there is a thermodynamic potential—the thermodynamic capacity—that quantifies the minimal work required to transform one macroscopic set of channels into another.

## Prospects for the thermodynamic capacity

Resource theories that are reversible are pretty rare. Reversibility is a coveted property because a reversible resource theory is one in which we can easily understand exactly which transformations are possible. Other than the thermodynamic resource theory of states mentioned above, most instances of a resource theory—especially resource theories of channels—typically produce the kind of overheads in the conversion cost that spoil reversibility. So it’s rather exciting when you do find a new reversible resource theory of channels.

Quantum information theorists, especially those working on the theory of quantum communication, care a lot about characterizing the capacity of a channel. This is the maximal amount of information that can be transmitted through a channel. Even though in our case we’re talking about a different kind of capacity—one where we transmit thermodynamic energy and entropy, rather than quantum bits of messages—there are some close parallels between the two settings from which both fields of quantum communication and quantum thermodynamics can profit. Our result draws deep inspiration from the so-called quantum reverse Shannon theorem, an important result in quantum communication that tells us how two parties can communicate using one kind of a channel if they have access to another kind of a channel. On the other hand, the thermodynamic capacity at zero energy is a quantity that was already studied in quantum communication, but it was not clear what that quantity represented concretely. This quantity gained even more importance as it was identified as the entropy of a channel. Now, we see that this quantity has a thermodynamic interpretation. Also, the thermodynamic capacity has a simple definition, it is relatively easy to compute and it is additive—all desirable properties that other measures of capacity of a quantum channel do not necessarily share.

We still have a few rough edges that I hope we can resolve sooner or later. In fact, there is an important caveat that I have avoided mentioning so far—our argument only holds for special kinds of channels, those that do the same thing regardless of when they are applied in time. (Those channels are called time-covariant.) A lot of channels that we’re used to studying have this property, but we think it should be possible to prove a version of our result for any general quantum channel. In fact, we do have another argument that works for all quantum channels, but it uses a slightly different thermodynamic framework which might not be physically well-grounded.

That’s all very nice, I can hear you think, but is this useful for any quantum computing applications? The truth is, we’re still pretty far from founding a new quantum start-up. The levels of heat dissipation in quantum logic elements are still orders of magnitude away from the fundamental limits that we study in the thermodynamic resource theory.

Rather, our result teaches us about the interplay of quantum channels and thermodynamic concepts. We not only have gained useful insight on the structure of quantum channels, but also developed new tools for how to analyze them. These will be useful to study more involved resource theories of channels. And still, in the future when quantum technologies will perhaps approach the thermodynamically reversible limit, it might be good to know how to implement a given quantum channel in such a way that good accuracy is guaranteed for any possible quantum input state, and without any inherent overhead due to the fact that we don’t know what the input state is.

Thermodynamics, a theory developed to study gases and steam engines, has turned out to be relevant from the most obvious to the most unexpected of situations—chemical reactions, electromagnetism, solid state physics, black holes, you name it. Trust the laws of thermodynamics to surprise you again by applying to a setting you’d never imagined them to, like quantum channels.

# Quantum information in quantum cognition

Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care about progress. Whether quantum physics could influence cognition much.

Quantum physics influences cognition insofar as (i) quantum physics prevents atoms from imploding and (ii) implosion inhabits atoms from contributing to cognition. But most physicists believe that useful entanglement can’t survive in brains. Entanglement consists of correlations shareable by quantum systems and stronger than any achievable by classical systems. Useful entanglement dies quickly in hot, wet, random environments.

Brains form such environments. Imagine injecting entangled molecules A and B into someone’s brain. Water, ions, and other particles would bombard the molecules. The higher the temperature, the heavier the bombardment. The bombardiers would entangle with the molecules via electric and magnetic fields. Each molecule can share only so much entanglement. The more A entangled with the environment, the less A could remain entangled with B. A would come to share a tiny amount of entanglement with each of many particles. Such tiny amounts couldn’t accomplish much. So quantum physics seems unlikely to affect cognition significantly.

Do not touch.

Yet my PhD advisor, John Preskill, encouraged me to consider whether the possibility interested me.

Try some completely different research, he said. Take a risk. If it doesn’t pan out, fine. People don’t expect much of grad students, anyway. Have you seen Matthew Fisher’s paper about quantum cognition?

Matthew Fisher is a theoretical physicist at the University of California, Santa Barbara. He has plaudits out the wazoo, many for his work on superconductors. A few years ago, Matthew developed an interest in biochemistry. He knew that most physicists doubt whether quantum physics could affect cognition much. But suppose that it could, he thought. How could it? Matthew reverse-engineered a mechanism, in a paper published by Annals of Physics in 2015.

A PhD student shouldn’t touch such research with a ten-foot radio antenna, says conventional wisdom. But I trust John Preskill in a way in which I trust no one else on Earth.

I’ll look at the paper, I said.

Matthew proposed that quantum physics could influence cognition as follows. Experimentalists have performed quantum computation using one hot, wet, random system: that of nuclear magnetic resonance (NMR). NMR is the process that underlies magnetic resonance imaging (MRI), a technique used to image people’s brains. A common NMR system consists of high-temperature liquid molecules. The molecules consists of atoms whose nuclei have quantum properties called spin. The nuclear spins encode quantum information (QI).

Nuclear spins, Matthew reasoned, might store QI in our brains. He catalogued the threats that could damage the QI. Hydrogen ions, he concluded, would threaten the QI most. They could entangle with (decohere) the spins via dipole-dipole interactions.

How can a spin avoid the threats? First, by having a quantum number $s = 1/2$. Such a quantum number zeroes out the nuclei’s electric quadrupole moments. Electric-quadrupole interactions can’t decohere such spins. Which biologically prevalent atoms have $s = 1/2$ nuclear spins? Phosphorus and hydrogen. Hydrogen suffers from other vulnerabilities, so phosphorus nuclear spins store QI in Matthew’s story. The spins serve as qubits, or quantum bits.

How can a phosphorus spin avoid entangling with other spins via magnetic dipole-dipole interactions? Such interactions depend on the spins’ orientations relative to their positions. Suppose that the phosphorus occupies a small molecule that tumbles in biofluids. The nucleus’s position changes randomly. The interaction can average out over tumbles.

The molecule contains atoms other than phosphorus. Those atoms have nuclei whose spins can interact with the phosphorus spins, unless every threatening spin has a quantum number $s = 0$. Which biologically prevalent atoms have $s = 0$ nuclear spins? Oxygen and calcium. The phosphorus should therefore occupy a molecule with oxygen and calcium.

Matthew designed this molecule to block decoherence. Then, he found the molecule in the scientific literature. The structure, ${\rm Ca}_9 ({\rm PO}_4)_6$, is called a Posner cluster or a Posner molecule. I’ll call it a Posner, for short. Posners appear to exist in simulated biofluids, fluids created to mimic the fluids in us. Posners are believed to exist in us and might participate in bone formation. According to Matthew’s estimates, Posners might protect phosphorus nuclear spins for up to 1-10 days.

Posner molecule (image courtesy of Swift et al.)

How can Posners influence cognition? Matthew proposed the following story.

Adenosine triphosphate (ATP) is a molecule that fuels biochemical reactions. “Triphosphate” means “containing three phosphate ions.” Phosphate (${\rm PO}_4^{3-}$) consists of one phosphorus atom and three oxygen atoms. Two of an ATP molecule’s phosphates can break off while remaining joined to each other.

The phosphate pair can drift until encountering an enzyme called pyrophosphatase. The enzyme can break the pair into independent phosphates. Matthew, with Leo Radzihovsky, conjectured that, as the pair breaks, the phosphorus nuclear spins are projected onto a singlet. This state, represented by $\frac{1}{ \sqrt{2} } ( | \uparrow \downarrow \rangle - | \downarrow \uparrow \rangle )$, is maximally entangled.

Imagine many entangled phosphates in a biofluid. Six phosphates can join nine calcium ions to form a Posner molecule. The Posner can share up to six singlets with other Posners. Clouds of entangled Posners can form.

One clump of Posners can enter one neuron while another clump enters another neuron. The protein VGLUT, or BNPI, sits in cell membranes and has the potential to ferry Posners in. The neurons will share entanglement. Imagine two Posners, P and Q, approaching each other in a neuron N. Quantum-chemistry calculations suggest that the Posners can bind together. Suppose that P shares entanglement with a Posner P’ in a neuron N’, while Q shares entanglement with a Posner Q’ in N’. The entanglement, with the binding of P to Q, can raise the probability that P’ binds to Q’.

Bound-together Posners will move slowly, having to push much water out of the way. Hydrogen and magnesium ions can latch onto the slow molecules easily. The Posners’ negatively charged phosphates will attract the ${\rm H}^+$ and ${\rm Mg}^{2+}$ as the phosphates attract the Posner’s ${\rm Ca}^{2+}$. The hydrogen and magnesium can dislodge the calcium, breaking apart the Posners. Calcium will flood neurons N and N’. Calcium floods a neuron’s axion terminal (the end of the neuron) when an electrical signal reaches the axion. The flood induces the neuron to release neurotransmitters. Neurotransmitters are chemicals that travel to the next neuron, inducing it to fire. So entanglement between phosphorus nuclear spins in Posner molecules might stimulate coordinated neuron firing.

Does Matthew’s story play out in the body? We can’t know till running experiments and analyzing the results. Experiments have begun: Last year, the Heising-Simons Foundation granted Matthew and collaborators \$1.2 million to test the proposal.

Suppose that Matthew conjectures correctly, John challenged me, or correctly enough. Posner molecules store QI. Quantum systems can process information in ways in which classical systems, like laptops, can’t. How adroitly can Posners process QI?

I threw away my iron-tipped medieval lance in year five of my PhD. I left Caltech for a five-month fellowship, bent on returning with a paper with which to answer John. I did, and Annals of Physics published the paper this month.

I had the fortune to interest Elizabeth Crosson in the project. Elizabeth, now an assistant professor at the University of New Mexico, was working as a postdoc in John’s group. Both of us are theorists who specialize in QI theory. But our backgrounds, skills, and specialties differ. We complemented each other while sharing a doggedness that kept us emailing, GChatting, and Google-hangout-ing at all hours.

Elizabeth and I translated Matthew’s biochemistry into the mathematical language of QI theory. We dissected Matthew’s narrative into a sequence of biochemical steps. We ascertained how each step would transform the QI encoded in the phosphorus nuclei. Each transformation, we represented with a piece of math and with a circuit-diagram element. (Circuit-diagram elements are pictures strung together to form circuits that run algorithms.) The set of transformations, we called Posner operations.

Imagine that you can perform Posner operations, by preparing molecules, trying to bind them together, etc. What QI-processing tasks can you perform? Elizabeth and I found applications to quantum communication, quantum error detection, and quantum computation. Our results rest on the assumption—possibly inaccurate—that Matthew conjectures correctly. Furthermore, we characterized what Posners could achieve if controlled. Randomness, rather than control, would direct Posners in biofluids. But what can happen in principle offers a starting point.

First, QI can be teleported from one Posner to another, while suffering noise.1 This noisy teleportation doubles as superdense coding: A trit is a random variable that assumes one of three possible values. A bit is a random variable that assumes one of two possible values. You can teleport a trit from one Posner to another effectively, while transmitting a bit directly, with help from entanglement.

Second, Matthew argued that Posners’ structures protect QI. Scientists have developed quantum error-correcting and -detecting codes to protect QI. Can Posners implement such codes, in our model? Yes: Elizabeth and I (with help from erstwhile Caltech postdoc Fernando Pastawski) developed a quantum error-detection code accessible to Posners. One Posner encodes a logical qutrit, the quantum version of a trit. The code detects any error that slams any of the Posner’s six qubits.

Third, how complicated an entangled state can Posner operations prepare? A powerful one, we found: Suppose that you can measure this state locally, such that earlier measurements’ outcomes affect which measurements you perform later. You can perform any quantum computation. That is, Posner operations can prepare a state that fuels universal measurement-based quantum computation.

Finally, Elizabeth and I quantified effects of entanglement on the rate at which Posners bind together. Imagine preparing two Posners, P and P’, that share entanglement only with other particles. If the Posners approach each other with the right orientation, they have a 33.6% chance of binding, in our model. Now, suppose that every qubit in P is maximally entangled with a qubit in P’. The binding probability can rise to 100%.

Elizabeth and I recast as a quantum circuit a biochemical process discussed in Matthew Fisher’s 2015 paper.

I feared that other scientists would pooh-pooh our work as crazy. To my surprise, enthusiasm flooded in. Colleagues cheered the risk on a challenge in an emerging field that perks up our ears. Besides, Elizabeth’s and my work is far from crazy. We don’t assert that quantum physics affects cognition. We imagine that Matthew conjectures correctly, acknowledging that he might not, and explore his proposal’s implications. Being neither biochemists nor experimentalists, we restrict our claims to QI theory.

Maybe Posners can’t protect coherence for long enough. Would inaccuracy of Matthew’s beach our whale of research? No. Posners prompted us to propose ideas and questions within QI theory. For instance, our quantum circuits illustrate interactions (unitary gates, to experts) interspersed with measurements implemented by the binding of Posners. The circuits partially motivated a subfield that emerged last summer and is picking up speed: Consider interspersing random unitary gates with measurements. The unitaries tend to entangle qubits, whereas the measurements disentangle. Which influence wins? Does the system undergo a phase transition from “mostly entangled” to “mostly unentangled” at some measurement frequency? Researchers from Santa Barbara to Colorado; MIT; Oxford; Lancaster, UK; Berkeley; Stanford; and Princeton have taken up the challenge.

A physics PhD student, conventional wisdom says, shouldn’t touch quantum cognition with a Swiss guard’s halberd. I’m glad I reached out: I learned much, contributed to science, and had an adventure. Besides, if anyone disapproves of daring, I can blame John Preskill.

Annals of Physics published “Quantum information in the Posner model of quantum cognition” here. You can find the arXiv version here and can watch a talk about our paper here.

1Experts: The noise arises because, if two Posners bind, they effectively undergo a measurement. This measurement transforms a subspace of the two-Posner Hilbert space as a coarse-grained Bell measurement. A Bell measurement yields one of four possible outcomes, or two bits. Discarding one of the bits amounts to coarse-graining the outcome. Quantum teleportation involves a Bell measurement. Coarse-graining the measurement introduces noise into the teleportation.

# Long live Yale’s cemetery

Call me morbid, but, the moment I arrived at Yale, I couldn’t wait to visit the graveyard.

I visited campus last February, to present the Yale Quantum Institute (YQI) Colloquium. The YQI occupies a building whose stone exterior honors Yale’s Gothic architecture and whose sleekness defies it. The YQI has theory and experiments, seminars and colloquia, error-correcting codes and small-scale quantum computers, mugs and laptop bumper stickers. Those assets would have drawn me like honey. But my host, Steve Girvin, piled molasses, fudge, and cookie dough on top: “you should definitely reserve some time to go visit Josiah Willard Gibbs, Jr., Lars Onsager, and John Kirkwood in the Grove Street Cemetery.”

Gibbs, Onsager, and Kirkwood pioneered statistical mechanics. Statistical mechanics is the physics of many-particle systems, energy, efficiency, and entropy, a measure of order. Statistical mechanics helps us understand why time flows in only one direction. As a colleague reminded me at a conference about entropy, “You are young. But you will grow old and die.” That conference featured a field trip to a cemetery at the University of Cambridge. My next entropy-centric conference took place next to a cemetery in Banff, Canada. A quantum-thermodynamics conference included a tour of an Oxford graveyard.1 (That conference reincarnated in Santa Barbara last June, but I found no cemeteries nearby. No wonder I haven’t blogged about it.) Why shouldn’t a quantum-thermodynamics colloquium lead to the Grove Street Cemetery?

Home of the Yale Quantum Institute

The Grove Street Cemetery lies a few blocks from the YQI. I walked from the latter to the former on a morning whose sunshine spoke more of springtime than of February. At one entrance stood a gatehouse that looked older than many of the cemetery’s residents.

“Can you tell me where to find Josiah Willard Gibbs?” I asked the gatekeepers. They handed me a map, traced routes on it, and dispatched me from their lodge. Snow had fallen the previous evening but was losing its battle against the sunshine. I sloshed to a pathway labeled “Locust,” waded along Locust until passing Myrtle, and splashed back and forth until a name caught my eye: “Gibbs.”

One entrance of the Grove Street Cemetery

Josiah Willard Gibbs stamped his name across statistical mechanics during the 1800s. Imagine a gas in a box, a system that illustrates much of statistical mechanics. Suppose that the gas exchanges heat with a temperature-$T$ bath through the box’s walls. After exchanging heat for a long time, the gas reaches thermal equilibrium: Large-scale properties, such as the gas’s energy, quit changing much. Imagine measuring the gas’s energy. What probability does the measurement have of outputting $E$? The Gibbs distribution provides the answer, $e^{ - E / (k_{\rm B} T) } / Z$. The $k_{\rm B}$ denotes Boltzmann’s constant, a fundamental constant of nature. The $Z$ denotes a partition function, which ensures that the probabilities sum to one.

Gibbs lent his name to more than probabilities. A function of probabilities, the Gibbs entropy, prefigured information theory. Entropy features in the Gibbs free energy, which dictates how much work certain thermodynamic systems can perform. A thermodynamic system has many properties, such as temperature and pressure. How many can you control? The answer follows from the Gibbs-Duheim relation. You’ll be able to follow the Gibbs walk, a Yale alumnus tells me, once construction on Yale’s physical-sciences complex ends.

Back I sloshed along Locust Lane. Turning left onto Myrtle, then right onto Cedar, led to a tree that sheltered two tombstones. They looked like buddies about to throw their arms around each other and smile for a photo. The lefthand tombstone reported four degrees, eight service positions, and three scientific honors of John Gamble Kirkwood. The righthand tombstone belonged to Lars Onsager:

NOBEL LAUREATE*

[ . . . ]

*ETC.

Onsager extended thermodynamics beyond equilibrium. Imagine gently poking one property of a thermodynamic system. For example, recall the gas in a box. Imagine connecting one end of the box to a temperature-$T$ bath and the other end to a bath at a slightly higher temperature, $T' \gtrsim T$. You’ll have poked the system’s temperature out of equilibrium. Heat will flow from the hotter bath to the colder bath. Particles carry the heat, energy of motion. Suppose that the particles have electric charges. An electric current will flow because of the temperature difference. Similarly, heat can flow because of an electric potential difference, or a pressure difference, and so on. You can cause a thermodynamic system’s elbow to itch, Onsager showed, by tickling the system’s ankle.

To Onsager’s left lay John Kirkwood. Kirkwood had defined a quasiprobability distribution in 1933. Quasiprobabilities resemble probabilities but can assume negative and nonreal values. These behaviors can signal nonclassical physics, such as the ability to outperform classical computers. I generalized Kirkwood’s quasiprobability with collaborators. Our generalized quasiprobability describes quantum chaos, thermalization, and the spread of information through entanglement. Applying the quasiprobability across theory and experiments has occupied me for two-and-a-half years. Rarely has a tombstone pleased anyone as much as Kirkwood’s tickled me.

The Grove Street Cemetery opened my morning with a whiff of rosemary. The evening closed with a shot of adrenaline. I met with four undergrad women who were taking Steve Girvin’s course, an advanced introduction to physics. I should have left the conversation bled of energy: Since visiting the cemetery, I’d held six discussions with nine people. But energy can flow backward. The students asked how I’d come to postdoc at Harvard; I asked what they might major in. They described the research they hoped to explore; I explained how I’d constructed my research program. They asked if I’d had to work as hard as they to understand physics; I confessed that I might have had to work harder.

I left the YQI content, that night. Such a future deserves its past; and such a past, its future.

With thanks to Steve Girvin, Florian Carle, and the Yale Quantum Institute for their hospitality.

1Thermodynamics is a physical theory that emerges from statistical mechanics.

# Symmetries and quantum error correction

It’s always exciting when you can bridge two different physical concepts that seem to have nothing in common—and it’s even more thrilling when the results have as broad a range of possible fields of application as from fault-tolerant quantum computation to quantum gravity.

Physicists love to draw connections between distinct ideas, interconnecting concepts and theories to uncover new structure in the landscape of scientific knowledge. Put together information theory with quantum mechanics and you’ve opened a whole new field of quantum information theory. More recently, machine learning tools have been combined with many-body physics to find new ways to identify phases of matter, and ideas from quantum computing were applied to Pozner molecules to obtain new plausible models of how the brain might work.

In a recent contribution, my collaborators and I took a shot at combining the two physical concepts of quantum error correction and physical symmetries. What can we say about a quantum error-correcting code that conforms to a physical symmetry? Surprisingly, a continuous symmetry prevents the code from doing its job: A code can conform well to the symmetry, or it can correct against errors accurately, but it cannot do both simultaneously.

By a continuous symmetry, we mean a transformation that is characterized by a set of continuous parameters, such as angles. For instance, if I am holding an atom in my hand (more realistically, it’ll be confined in some fancy trap with lots of lasers), then I can rotate it around and about in space:

A rotation like this is fully specified by an axis and an angle, which are continuous parameters. Other transformations that we could think of are, for instance, time evolution, or a continuous family of unitary gates that we might want to apply to the system.

On the other hand, a code is a way of embedding some logical information into physical systems:

By cleverly distributing the information that we care about over several physical systems, an error-correcting code is able to successfully recover the original logical information even if the physical systems are exposed to some noise. Quantum error-correcting codes are particularly promising for quantum computing, since qubits tend to lose their information really fast (current typical ones can hold their information for a few seconds). In this way, instead of storing the actual information we care about on a single qubit, we use extra qubits which we prepare in a complicated state that is designed to protect this information from the noise.

## Covariant codes for quantum computation

A code that is compatible with respect to a physical symmetry is called covariant. This property ensures that if I apply a symmetry transformation on the logical information, this is equivalent to applying corresponding symmetry transformations on each of the physical systems.

Suppose I would like to flip my qubit from “0” to “1” and from “1” to “0”. If my information is stored in an encoded form, then in principle I first need to decode the information to uncover the original logical information, apply the flip operation, and then re-encode the new logical information back onto the physical qubits. A covariant code allows to perform the transformation directly on the physical qubits, without having to decode the information first:

The advantage of this scheme is that the logical information is never exposed and remains protected all along the computation.

But here’s the catch: Eastin and Knill famously proved that error-correcting codes can be at most covariant with respect to a finite set of transformations, ruling out universal computation with transversal gates. In other words, the computations we can perform using this scheme are very limited because we can’t perform any continuous symmetry transformation.

Interestingly, however, there’s a loophole: If we consider macroscopic systems, such as a particle with a very large value of spin, then it becomes possible again to construct codes that are covariant with respect to continuous transformations.

How is that possible, you ask? How do we transition from the microscopic regime, where covariant codes are ruled out for continuous symmetries, to the macroscopic regime, where they are allowed? We provide an answer by resorting to approximate quantum error correction. Namely, we consider the situation where the code does not have to correct each error exactly, but only has to reconstruct a good approximation of the logical information. As it turns out, there is a quantitative limit to how accurately a code can correct against errors if it is covariant with respect to a continuous symmetry, represented by the following equation:

where specifies how inaccurately the code error-corrects ( means the code can correct against errors perfectly), n is the number of physical subsystems, and the and are measures of “how strongly” the symmetry transformation can act on the logical and physical subsystems.

Let’s try to understand the right-hand side of this equation. In physics, continuous symmetries are generated by what we call physical charges. These are physical quantities that are associated with the symmetry, and that characterize how the symmetry acts on each state of the system. For instance, the charge that corresponds to time evolution is simply energy: States that label high energies have a rapidly varying phase whereas the phase of low-energy states changes slowly in time. Above, we indicate by the range of possible charge values on the logical system and by the corresponding range of charge values on each physical subsystem. In typical settings, this range of charge values is related to the dimension of the system—the more states the system has, intuitively, the greater range of charges it can accommodate.

The above equation states that the inaccuracy of the code must be larger than some value given on the right-hand side of the equation, which depends on the number of subsystems n and the ranges of charge values on the logical system and physical subsystems. The right-hand side becomes small in two regimes: if each subsystem can accommodate a large range of charge values, or if there is a large number of physical systems. In these regimes, our limitation vanishes, and we can circumvent the Eastin-Knill theorem and construct good covariant error-correcting codes. This allows us to connect the two regimes that seemed incompatible earlier, the microscopic regime where there cannot be any covariant codes, and the macroscopic regime where they are allowed.

## From quantum computation to many-body physics and quantum gravity

Quantum error-correcting codes not only serve to protect information in a quantum computation against noise, but they also provide a conceptual toolbox to understand complex physical systems where a quantum state is delocalized over many physical subsystems. The tight connections between quantum error correction and many-body physics have been put to light following a long history of pioneering research at Caltech in these fields. And as if that weren’t enough, quantum error correcting codes were also shown to play a crucial role in understanding quantum gravity.

There is an abundance of natural physical symmetries to consider both in many-body physics and in quantum gravity, and that gives us a good reason to be excited about characterizing covariant codes. For instance, there are natural approximate quantum error correcting codes that appear in some statistical mechanical models by cleverly picking global energy eigenstates. These codes are covariant with respect to time evolution by construction, since the codewords are energy eigenstates. Now, we understand more precisely under which conditions such codes can be constructed.

Perhaps an even more illustrative example is that of time evolution in holographic quantum gravity, that is, in the AdS/CFT correspondence. This model of quantum gravity has the property that it is equivalent to a usual quantum field theory that lives on the boundary of the universe. What’s more, the correspondence which tells us how the bulk quantum gravity theory is mapped to the boundary is, in fact, a quantum error-correcting code. If we add a time axis, then the picture becomes a cylinder where the interior is the theory of quantum gravity, and where the cylinder itself represents a traditional quantum field theory:

Since the bulk theory and the boundary theory are equivalent, the action of time evolution must be faithfully represented in both pictures. But this is in apparent contradiction with the Eastin-Knill theorem, from which it follows that a quantum error-correcting code cannot be covariant with respect to a continuous symmetry. We now understand how this is, in fact, not a contradiction: As we’ve seen, codes may be covariant with respect to continuous symmetries in the presence of systems with a large number of degrees of freedom, such as a quantum field theory.

## What’s next?

There are some further results in our paper that I have not touched upon in this post, including a precise approximate statement of the Eastin-Knill theorem in terms of system dimensions, and a fun machinery to construct covariant codes for more general systems such as oscillators and rotors.

We have only scratched the surface of the different applications I’ve mentioned, by studying the properties of covariant codes in general. I’m now excited to dive into more detail with our wonderful team to study deeper applications to correlations in many-body systems, global symmetries in quantum gravity, accuracy limits of quantum clocks and precision limits to quantum metrology in the presence of noise.

This has been an incredibly fun project to work on. Such a collaboration illustrates again the benefit of interacting with great scientists with a wide range of areas of expertise including representation theory, continuous variable systems, and quantum gravity. Thanks Sepehr, Victor, Grant, Fernando, Patrick, and John, for this fantastic experience.

# My QIP 2019 After-Dinner Speech

Scientists who work on theoretical aspects of quantum computation and information look forward each year to the Conference on Quantum Information Processing (QIP), an annual event since 1998. This year’s meeting, QIP 2019, was hosted this past week by the University of Colorado at Boulder. I attended and had a great time, as I always do.

But this year, in addition to catching up with old friends and talking with colleagues about the latest research advances, I also accepted a humbling assignment: I was the after-dinner speaker at the conference banquet. Here is (approximately) what I said.

QIP 2019 After-Dinner Speech
16 January 2019

Thanks, it’s a great honor to be here, and especially to be introduced by Graeme Smith, my former student. I’m very proud of your success, Graeme. Back in the day, who would have believed it?

And I’m especially glad to join you for these holiday festivities. You do know this is a holiday, don’t you? Yes, as we do every January, we are once again celebrating Gottesman’s birthday! Happy Birthday, Daniel!

Look, I’m kidding of course. Yes, it really is Daniel’s birthday — and I’m sure he appreciates 500 people celebrating in his honor — but I know you’re really here for QIP. We’ve been holding this annual celebration of Quantum Information Processing since 1998 — this is the 22nd QIP. If you are interested in the history of this conference, it’s very helpful that the QIP website includes links to the sites for all previous QIPs. I hope that continues; it conveys a sense of history. For each of those past meetings, you can see what people were talking about, who was there, what they looked like in the conference photo, etc.

Some of you were there the very first time – I was not. But among the attendees at the first QIP, in Arhus in 1998, where a number of brilliant up-and-coming young scientists who have since then become luminaries of our field. Including: Dorit Aharonov, Wim van Dam, Peter Hoyer (who was an organizer), Michele Mosca, John Smolin, Barbara Terhal, and John Watrous. Also somewhat more senior people were there, like Harry Buhrman and Richard Cleve. And pioneers so eminent that we refer to them by their first names alone:  Umesh … Gilles … Charlie. It’s nice to know those people are still around, but it validates the health of our field that so many new faces are here, that so many young people are still drawn to QIP, 21 years after it all began. Over 300 students and postdocs are here this year, among nearly 500 attendees.

QIP has changed since the early days. It was smaller and more informal then; the culture was more like a theoretical physics conference, where the organizing committee brainstorms and conjures up a list of invited speakers. The system changed in 2006, when for the first time there were submissions and a program committee. That more formal system opened up opportunities to speak to a broader community, and the quality of the accepted talks has stayed very high — only 18% of 349 submissions were accepted this year.

In fact it has become a badge of honor to speak here — people put it on their CVs: “I gave a QIP contributed talk, or plenary talk, or invited talk.” But what do you think is the highest honor that QIP can bestow? Well, it’s obvious isn’t it? It’s the after-dinner speech! That’s the talk to rule them all. So Graeme told me, when he invited me to do this. And I checked, Gottesman put it on his website, and everyone knows Daniel is a very serious guy. So it must be important. Look, we’re having a banquet in honor of his birthday, and he can hardly crack a smile!

I hear the snickers. I know what you’re thinking. “John, wake up. Don’t you see what Graeme was trying to tell you: You’re too washed up to get a talk accepted to QIP! This is the only way to get you on the program now!” But no, you’re wrong. Graeme told me this is a great honor. And I trust Graeme. He’s an honest man. What? Why are you laughing? It’s true.

I asked Graeme, what should I talk about? He said, “Well, you might try to be funny.” I said, “What do you mean funny? You mean funny Ha Ha? Or do you mean funny the way cheese smells when it’s been in the fridge for too long?” He said, “No I mean really, really funny. You know, like Scott.”

So there it was, the gauntlet had been thrown. Some of you are too young to remember this, but the most notorious QIP after-dinner speech of them all was Scott Aaronson’s in Paris in 2006. Were you there? He used props, and he skewered his more senior colleagues with razor sharp impressions. And remember, this was 2006, so everybody was Scott’s more senior colleague. He was 12 at the time, if memory serves.

He killed. Even I appreciated some of the jokes; for example, as a physicist I could understand this one: Scott said, “I don’t care about the fine structure constant, it’s just a constant.” Ba ding!  So Scott set the standard back then, and though many have aspired to clear the bar since then, few have come close.

But remember, this was Graeme I was talking to. And I guess many of you know that I’ve had a lot of students through the years, and I’m proud of all of them. But my memory isn’t what it once was; I need to use mnemonic tricks to keep track of them now. So I have a rating system;  I rate them according to how funny they are. And Graeme is practically off the chart, that’s how funny he is. But his is what I call stealth humor. You can’t always tell that he’s being funny, but you assume it.

So I said, “Graeme, What’s the secret? Teach me how to be funny.” I meant it sincerely, and he responded sympathetically. Graeme said, “Well, if you want to be funny, you have to believe you are funny. So when I want to be funny, I think of someone who is funny, and I pretend to be that person.” I said, “Aha, so you go out there and pretend to be Graeme Smith?” And Graeme said, “No, that wouldn’t work for me. I close my eyes and pretend I’m … John Smolin!” I said, “Graeme, you mean you want me to be indistinguishable from John Smolin to an audience of computationally bounded quantum adversaries?” He nodded. “But Graeme, I don’t know any plausible cryptographic assumptions under which that’s possible!”

Fortunately, I had another idea. “I write poems,” I said. “What if I recite a poem? This would set a great precedent. From now on, everyone would know: the QIP after-dinner speech will be a poetry slam!”

Graeme replied “Well, that sounds [long pause] really [pause] boring. But how about a limerick? People love limericks.” I objected, “Graeme, I don’t do limericks. I’m not good at limericks.” But he wouldn’t back down. “Try a limerick,” Graeme said. “People like limericks. They’re so [pause] short.”

But I don’t do limericks. You see:

I was invited to speak here by Graeme.
He knows me well, just as I am.
He was really quite nice
Please don’t do a poetry slam.

Well, like I said, I don’t do limericks.

So now I’m starting to wonder: Why did they invite me to do this anyway? And I think I figured that out. See, Graeme asked me to speak just a few days ago. This must be what happened. Like any smoothly functioning organizing committee, they lined up an after-dinner speaker months in advance, as is the usual practice.

But then, just a few days before the conference began, they began to worry. “We better comb through the speaker’s Twitter feed. Maybe, years ago, our speaker said something offensive, something disqualifying.” And guess what? They found something, something really bad. It turned out that the designated after-dinner speaker had once made a deeply offensive remark about something called “quantum supremacy” … No, wait … that can’t be it.

Can’t you picture the panicky meeting of the organizers? QIP is about to start, and there’s no after-dinner speaker! So people started throwing out suggestions, starting with the usual suspects.

“No, he’s booked.”
“Are you telling me Schroedinger’s Rat has another gig that same night?”
“No, no, I mean they booked him.  A high-profile journal filed a complaint and he’s in the slammer.”
“No, same problem.”

“I’ve got it,” someone says: “How about the hottest quantum Twitter account out there? Yes, I’m talking about Quantum Computing Memes for QMA-Complete Teens!”

Are you all following that account? You should be. That’s where I go for all the latest fast-breaking quantum news. And that’s where you can get advice about what a quantumist should wear on Halloween. Your costume should combine Sexy with your greatest fear.  Right, I mean Sexy P = BQP.

Hey does that worry you? That maybe P = BQP? Does it keep you up at night? It’s possible, isn’t it? But it doesn’t worry me much. If it turns out that P = BQP, I’m just going to make up another word. How about NISP? Noisy Intermediate-Scale Polynomial.

I guess they weren’t able to smoke out whoever is behind Quantum Computing Memes for QMA-Complete Teens. So here I am.

Aside from Limericks, Graeme had another suggestion. He said, “You can reminisce. Tell us what QIP was like in the old days.” “The old days?” I said. “Yes, you know. You could be one of those stooped-over white-haired old men who tells interminable stories that nobody cares about.” I hesitated. “Yeah, I think I could do that.”

Okay, if that’s what you want, I’ll tell a story about my first QIP; that was QIP 2000, which was actually in Montreal in December 1999. It was back in the BPC era — Before Program Committee — and I was an invited speaker (I talked about decoding the toric code). Attending with me was Michael Nielsen, then a Caltech postdoc. Michael’s good friend Ike Chuang was also in the hotel, and they were in adjacent rooms. Both had brought laptops (not a given in 1999), and they wanted to share files. Well, hotels did not routinely offer Internet access back then, and certainly not wireless. But Ike had brought along a spool of Ethernet cable. So Ike and Mike both opened their windows, even though it was freezing cold. And Ike leaned out his window and made repeated attempts to toss the cable though Michael’s window before he finally succeeded, and they connected their computers.

I demanded to know, why the urgent need for a connection? And that was the day I found what most of the rest of the quantum world already knew: Mike and Ike were writing a book! By then they were in the final stages of writing, after some four years of effort (they sent the final draft of the book off to Cambridge University Press the following June).

So, QIP really has changed. The Mike and Ike book is out now. And it’s no longer necessary to open your window on a frigid Montreal evening to share a file with your collaborator.

Boy, it was cold that week in Montreal. [How cold was it?] Well, we went to lunch one day during the conference, and were walking single file down a narrow sidewalk toward the restaurant, when Harry Buhrman, who was right behind me, said: “John, there’s an icicle on your backpack!” You see, I hadn’t screwed the cap all the way shut on my water bottle, water was leaking out of the bottle, soaking through the backback, and immediately freezing on contact with the air; hence the icicle. And ever since then I’ve always been sure to screw my bottle cap shut tight. But over the years since then, lots of other things have spilled in my backpack just the same, and I’d love to tell you about that, but …

Well, my stories may be too lacking in drama to carry the evening ….  Look, I don’t care what Graeme says, I’m gonna recite some poems!

I can’t remember how this got started, but some years ago I started writing a poem whenever I needed to introduce a speaker at the Caltech physics colloquium. I don’t do this so much anymore. Partly because I realized that my poetry might reveal my disturbing innermost thoughts, which are best kept private.

Actually, one of my colleagues, after hearing one of my poems, suggested throwing the poem into a black hole. And when we tried it … boom …. it bounced right back, but in a highly scrambled form! And ever since then I’ve had that excuse. If someone says “That’s not such a great poem,” I can shoot back, “Yeah, but it was better before it got scrambled.”

But anyway, here’s one I wrote to honor Ben Schumacher, the pioneer of quantum information theory who named the qubit, and whose compression theorem you all know well.

Ben.
He rocks.
I remember
When
He showed me how to fit
A qubit
In a small box.

I wonder how it feels
To be compressed.
And then to pass
A fidelity test.
Or does it feel
At all, and if it does
Would I squeal
Or be just as I was?

If not undone
I’d become as I’d begun
And write a memorandum
On being random.
Had it felt like a belt
Of rum?

And might it be predicted
Longing for my session
Of compression?

I’d crawl
To Ben again.
And call,
Don’t stall!
Make me small!”

[Silence]

Yeah that’s the response I usually get when I recite this poem — embarrassed silence, followed by a few nervous titters.

So, as you can see, as in Ben Schumacher’s case, I use poetry to acknowledge our debt to the guiding intellects of our discipline. It doesn’t always work, though. I once tried to write a poem about someone I admire very much, Daniel Gottesman, and it started like this:

When the weather’s hottest, then
I call for Daniel Gottesman.
My apples are less spotted when
Daniel eats the rottenest ten …

It just wasn’t working, so I stopped there. Someday, I’ll go back and finish it. But it’s tough to rhyme “Gottesman.”

More apropos of QIP, some of you may recall that about 12 years ago, one of the hot topics was quantum speedups for formula evaluation, a subject ignited by a brilliant paper by Eddie Farhi, Jeffrey Goldstone, and Sam Gutmann. They showed there’s a polynomial speedup if we use a quantum computer to, say, determine whether a two-player game has a winning strategy. That breakthrough inspired me to write an homage to Eddie, which went:

We’re very sorry, Eddie Farhi
Can’t run it on those mean machines
Until we’ve actually got ‘em.

You’re not alone, so go on home,
Tell Jeffrey and tell Sam:
Come up with something classical
Or else it’s just a scam.

Unless … you think it’s on the brink
A quantum-cal device.
That solves a game and brings you fame.
Damn! That would be nice!

Now, one thing that Graeme explained to me is that the white-haired-old-man talk has a mandatory feature: It must go on too long. Maybe I have met that criterion by now. Except …

There’s one thing Graeme neglected to say. He never told me that I must not sing at QIP.

You see, there’s a problem: Tragically, though I like to sing, I don’t sing very well at all. And unfortunately, I am totally unaware of this fact. So I sometimes I sing in public, despite strongly worded advice not to do so.

When I was about to leave home on my way to QIP, my wife Roberta asked me, “When are you going to prepare your after-dinner talk?” I said, “Well, I guess I’ll work on it on the plane.” She said, “LA to Denver, that’s not a long enough flight.” I said, “I know!”

What I didn’t say, is that I was thinking of singing a song. If I had, Roberta would have tried to stop me from boarding the plane.

So I guess it’s up to you, what do you think? Should we stop here while I’m (sort of) ahead, or should we take the plunge. Song or no song? How many say song?

All right, that’s good enough for me! This is a song that I usually perform in front of a full orchestra, and I hoped the Denver Symphony Orchestra would be here to back me up. But it turns out they don’t exist anymore. So I’ll just have to do my best.

If you are a fan of Rodgers and Hammerstein, you’ll recognize the tune as a butchered version of Some Enchanted Evening, But the lyrics have changed. This song is called One Entangled Evening.

One entangled evening
We will see a qubit
And another qubit
Across a crowded lab.

And somehow we’ll know
We’ll know even then
This qubit’s entangled
Aligned with its friend.

One entangled evening
We’ll cool down a circuit
See if we can work it
At twenty milli-K.

A circuit that cold
Is worth more than gold
For qubits within it.
Will do as they’re told.

Quantum’s inviting, just as Feynman knew.
The future’s exciting, if we see it through

One entangled evening
Anyons will be braiding
The noise that haunts the lab.

Then our quantum goods
Will work as they should
Solving the problems

Once we have dreamt it, we can make it so.
Once we have dreamt it, we can make it so!

The song lyrics are meant to be uplifting, and I admit they’re corny. No one can promise you that, in the words of another song, “the dreams that you dare to dream really do come true.” That’s not always the case.

At this time in the field of quantum information processing, there are very big dreams, and many of us worry about unrealistic expectations concerning the time scale for quantum computing to have a transformative impact on society. Progress will be incremental. New technology does not change the world all at once; it’s a gradual process.

But I do feel that from the perspective of the broad sweep of history, we (the QIP community and the broader quantum community) are very privileged to be working in this field at a pivotal time in the history of science and technology on earth. We should deeply cherish that good fortune, and the opportunities it affords. I’m confident that great discoveries lie ahead for us.

It’s been a great privilege for me to be a part of a thriving quantum community for more than 20 years. By now, QIP has become one of our venerable traditions, and I hope it continues to flourish for many years ahead. Now it’s up to all of you to make our quantum dreams come true. We are on a great intellectual adventure. Let’s savor it and enjoy it to the hilt!

Thanks for putting up with me tonight.

[And here’s proof that I really did sing.]

# Chasing Ed Jaynes’s ghost

You can’t escape him, working where information theory meets statistical mechanics.

Information theory concerns how efficiently we can encode information, compute, evade eavesdroppers, and communicate. Statistical mechanics is the physics of  many particles. We can’t track every particle in a material, such as a sheet of glass. Instead, we reason about how the conglomerate likely behaves. Since we can’t know how all the particles behave, uncertainty blunts our predictions. Uncertainty underlies also information theory: You can think that your brother wished you a happy birthday on the phone. But noise corroded the signal; he might have wished you a madcap Earth Day.

Edwin Thompson Jaynes united the fields, in two 1957 papers entitled “Information theory and statistical mechanics.” I’ve cited the papers in at least two of mine. Those 1957 papers, and Jaynes’s philosophy, permeate pockets of quantum information theory, statistical mechanics, and biophysics. Say you know a little about some system, Jaynes wrote, like a gas’s average energy. Say you want to describe the gas’s state mathematically. Which state can you most reasonably ascribe to the gas? The state that, upon satisfying the average-energy constraint, reflects our ignorance of the rest of the gas’s properties. Information theorists quantify ignorance with a function called entropy, so we ascribe to the gas a large-entropy state. Jaynes’s Principle of Maximum Entropy has spread from statistical mechanics to image processing and computer science and beyond. You can’t evade Ed Jaynes.

I decided to turn the tables on him this December. I was visiting to Washington University in St. Louis, where Jaynes worked until six years before his 1998 death. Haunted by Jaynes, I’d hunt down his ghost.

I began with my host, Kater Murch. Kater’s lab performs experiments with superconducting qubits. These quantum circuits sustain currents that can flow forever, without dissipating. I questioned Kater over hummus, the evening after I presented a seminar about quantum uncertainty and equilibration. Kater had arrived at WashU a decade-and-a-half after Jaynes’s passing but had kept his ears open.

Ed Jaynes, Kater said, consulted for a startup, decades ago. The company lacked the funds to pay him, so it offered him stock. That company was Varian, and Jaynes wound up with a pretty penny. He bought a mansion, across the street from campus, where he hosted the physics faculty and grad students every Friday. He’d play a grand piano, and guests would accompany him on instruments they’d bring. The department doubled as his family.

The library kept a binder of Jaynes’s papers, which Kater had skimmed the previous year. What clarity shined through those papers! With a touch of pride, Kater added that he inhabited Jaynes’s former office. Or the office next door. He wasn’t certain.

I passed the hummus to a grad student of Kater’s. Do you hear stories about Jaynes around the department? I asked. I’d heard plenty about Feynman, as a PhD student at Caltech.

Not many, he answered. Just in conversations like this.

Later that evening, I exchanged emails with Kater. A contemporary of Jaynes’s had attended my seminar, he mentioned. Pity that I’d missed meeting the contemporary.

The following afternoon, I climbed to the physics library on the third floor of Crow Hall. Portraits of suited men greeted me. At the circulation desk, I asked for the binders of Jaynes’s papers.

E.T. Jaynes, I repeated. He worked here as a faculty member.

She turned to her computer. Can you spell that?

I obeyed while typing the name into the computer for patrons. The catalogue proffered several entries, one of which resembled my target. I wrote down the call number, then glanced at the notes over which the student was bending: “The harmonic oscillator.” An undergrad studying physics, I surmised. Maybe she’ll encounter Jaynes in a couple of years.

I hiked upstairs, located the statistical-mechanics section, and ran a finger along the shelf. Hurt and Hermann, Itzykson and Drouffe, …Kadanoff and Baym. No Jaynes? I double-checked. No Jaynes.

Upon descending the stairs, I queried the student at the circulation desk. She checked the catalogue entry, then ahhhed. You’d have go to the main campus library for this, she said. Do you want directions? I declined, thanked her, and prepared to return to Kater’s lab. Calculations awaited me there; I’d have no time for the main library.

As I reached the physics library’s door, a placard caught my eye. It appeared to list the men whose portraits lined the walls. Arthur Compton…I only glanced at the placard, but I didn’t notice any “Jaynes.”

Arthur Compton greeted me also from an engraving en route to Kater’s lab. Down the hall lay a narrow staircase on whose installation, according to Kater, Jaynes had insisted. Physicists would have, in the stairs’ absence, had to trek down the hall to access the third floor. Of course I wouldn’t photograph the staircase for a blog post. I might belong to the millenial generation, but I aim and click only with purpose. What, though, could I report in a blog post?

That night, I googled “e.t. jaynes.” His Wikipedia page contained only introductory and “Notes” sections. A WashU website offered a biography and unpublished works. But another tidbit I’d heard in the department yielded no Google hits, at first glance. I forbore a second glance, navigated to my inbox, and emailed Kater about plans for the next day.

I’d almost given up on Jaynes when Kater responded. After agreeing to my suggestion, he reported feedback about my seminar: A fellow faculty member “thought that Ed Jaynes (his contemporary) would have been very pleased.”

The email landed in my “Nice messages” folder within two shakes.

Leaning back, I reevaluated my data about Jaynes. I’d unearthed little, and little surprise: According to the WashU website, Jaynes “would undoubtedly be uncomfortable with all of the attention being lavished on him now that he is dead.” I appreciate privacy and modesty. Nor does Jaynes need portraits or engravings. His legacy lives in ideas, in people. Faculty from across his department attended a seminar about equilibration and about how much we can know about quantum systems. Kater might or might not inhabit Jaynes’s office. But Kater wears a strip cut from Jaynes’s mantle: Kater’s lab probes the intersection of information theory and statistical mechanics. They’ve built a Maxwell demon, a device that uses information as a sort of fuel to perform thermodynamic work.

I’ve blogged about legacies that last. Assyrian reliefs carved in alabaster survive for millennia, as do ideas. Jaynes’s ideas thrive; they live even in me.

Did I find Ed Jaynes’s ghost at WashU? I think I honored it, by pursuing calculations instead of pursuing his ghost further. I can’t say whether I found his ghost. But I gained enough information.

With thanks to Kater and to the Washington University Department of Physics for their hospitality.

# I get knocked down…

“You’ll have to have a thick skin.”

Marcelo Gleiser, a college mentor of mine, emailed the warning. I’d sent a list of physics PhD programs and requested advice about which to attend. Marcelo’s and my department had fostered encouragement and consideration.

Suit up, Marcelo was saying.

Criticism fuels science, as Oxford physicist David Deutsch has written. We have choices about how we criticize. Some criticism styles reflect consideration for the criticized work’s creator. Tufts University philosopher Daniel Dennett has devised guidelines for “criticizing with kindness”:1

1. You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.

2. You should list any points of agreement (especially if they are not matters of general or widespread agreement).

3. You should mention anything you have learned from your target.

4. Only then are you permitted to say so much as a word of rebuttal or criticism.

Scientists skip to step four often—when refereeing papers submitted to journals, when posing questions during seminars, when emailing collaborators, when colleagues sketch ideas at a blackboard. Why? Listening and criticizing require time, thought, and effort—three of a scientist’s most valuable resources. Should any scientist spend those resources on an idea of mine, s/he deserves my gratitude. Spending empathy atop time, thought, and effort can feel supererogatory. Nor do all scientists prioritize empathy and kindness. Others of us prioritize empathy but—as I have over the past five years—grown so used to its latency, I forget to demonstrate it.

Doing science requires facing not only criticism, but also “That doesn’t make sense,” “Who cares?” “Of course not,” and other morale boosters.

Doing science requires resilience.

So do measurements of quantum information (QI) scrambling. Scrambling is a subtle, late, quantum stage of equilibration2 in many-body systems. Example systems include chains of spins,3 such as in ultracold atoms, that interact with each other strongly. Exotic examples include black holes in anti-de Sitter space.4

Imagine whacking one side of a chain of interacting spins. Information about the whack will disseminate throughout the chain via entanglement.5 After a long interval (the scrambling time, $t_*$), spins across the systems will share many-body entanglement. No measurement of any few, close-together spins can disclose much about the whack. Information will have scrambled across the system.

QI scrambling has the subtlety of an assassin treading a Persian carpet at midnight. Can we observe scrambling?

A Stanford team proposed a scheme for detecting scrambling using interferometry.6 Justin Dressel, Brian Swingle, and I proposed a scheme based on weak measurements, which refrain from disturbing the measured system much. Other teams have proposed alternatives.

Many schemes rely on effective time reversal: The experimentalist must perform the quantum analog of inverting particles’ momenta. One must negate the Hamiltonian $\hat{H}$, the observable that governs how the system evolves: $\hat{H} \mapsto - \hat{H}$.

At least, the experimentalist must try. The experimentalist will likely map $\hat{H}$ to $- \hat{H} + \varepsilon$. The small error $\varepsilon$ could wreak havoc: QI scrambling relates to chaos, exemplified by the butterfly effect. Tiny perturbations, such as the flap of a butterfly’s wings, can snowball in chaotic systems, as by generating tornadoes. Will the $\varepsilon$ snowball, obscuring observations of scrambling?

It needn’t, Brian and I wrote in a recent paper. You can divide out much of the error until $t_*$.

You can detect scrambling by measuring an out-of-time-ordered correlator (OTOC), an object I’ve effused about elsewhere. Let’s denote the time-$t$ correlator by $F(t)$. You can infer an approximation $\tilde{F}(t)$ to $F(t)$ upon implementing an $\varepsilon$-ridden interferometry or weak-measurement protocol. Remove some steps from that protocol, Brian and I say. Infer a simpler, easier-to-measure object $\tilde{F}_{\rm simple}(t)$. Divide the two measurement outcomes to approximate the OTOC:

$F(t) \approx \frac{ \tilde{F}(t) }{ \tilde{F}_{\rm simple}(t) }$.

OTOC measurements exhibit resilience to error.

Physicists need resilience. Brian criticizes with such grace, he could serve as the poster child for Daniel Dennett’s guidelines. But not every scientist could. How can we withstand kindness-lite criticism?

By drawing confidence from what we’ve achieved, with help from mentors like Marcelo. I couldn’t tell what about me—if anything—could serve as a rock on which to plant a foot, as an undergrad. Mentors identified what I had too little experience to appreciate. You question what you don’t understand, they said. You assimilate perspectives from textbooks, lectures, practice problems, and past experiences. You scrutinize details while keeping an eye on the big picture. So don’t let so-and-so intimidate you.

I still lack my mentors’ experience, but I’ve imbibed a drop of their insight. I savor calculations that I nail, congratulate myself upon nullifying referees’ concerns, and celebrate the theorems I prove.

I’ve also created an email folder entitled “Nice messages.” In go “I loved your new paper; combining those topics was creative,” “Well done on the seminar; I’m now thinking of exploring that field,” and other rarities. The folder affords an umbrella when physics clouds gather.

Finally, I try to express appreciation of others’ work.7 Science thrives on criticism, but scientists do science. And scientists are human—undergrads, postdocs, senior researchers, and everyone else.

Doing science—and attempting to negate Hamiltonians—we get knocked down. But we can get up again.

Around the time Brian and I released “Resilience” two other groups proposed related renormalizations. Check out their schemes here and here.

1Thanks to Sean Carroll for alerting me to this gem of Dennett’s.

2A system equilibrates as its large-scale properties, like energy, flatline.

3Angular-momentum-like quantum properties

4Certain space-times different from ours

5Correlations, shareable by quantum systems, stronger than any achievable by classical systems

6The cancellation (as by a crest of one wave and a trough of another) of components of a quantum state, or the addition of components (as two waves’ crests)

7Appreciation of specific qualities. “Nice job” can reflect a speaker’s belief but often reflects a desire to buoy a receiver whose work has few merits to elaborate on. I applaud that desire and recommend reinvesting it. “Nice job” carries little content, which evaporates under repetition. Specificity provides content: “Your idea is alluringly simple but could reverberate across multiple fields” has gristle.

# A quantum podcast

A few months ago I sat down with Craig Cannon of Y Combinator for a discussion about quantum technology and other things. A lightly edited version was published this week on the Y Combinator blog. The video is also on YouTube:

If you’re in a hurry, or can’t stand the sound of my voice, you might prefer to read the transcript, which is appended below. Only by watching the video, however, can you follow the waving of my hands.

I grabbed the transcript from the Y Combinator blog post, so you can read it there if you prefer, but I’ve corrected some of the typos. (There are a few references to questions and comments that were edited out, but that shouldn’t cause too much confusion.)

Here we go:

Craig Cannon [00:00:00] – Hey, how’s it going? This is Craig Cannon, and you’re listening to Y Combinator’s Podcast. Today’s episode is with John Preskill. John’s a theoretical physicist and the Richard P. Feynman Professor of Theoretical Physics at Caltech. He once won a bet with Stephen Hawking and he writes that it made him briefly almost famous. Basically, what happened is John and Kip Thorne bet that singularities could exist outside of black holes. After six years, Hawking conceded. He said that they were possible in very special, “non-generic conditions.” I’ll link up some more details to that in the description. In this episode, we cover what John’s been focusing on for years, which is quantum information, quantum computing, and quantum error correction. Alright, here we go. What was the revelation that made scientists and physicists think that a quantum computer could exist?

John Preskill [00:00:54] – It’s not obvious. A lot of people thought it couldn’t. The idea that a quantum computer would be powerful was emphasized over 30 years ago by Richard Feynman, the Caltech physicist. It was interesting how he came to that realization. Feynman was interested in computation his whole life. He had been involved during the war in Los Alamos. He was the head of the computation group. He was the guy who fixed the little mechanical calculators, and he had a whole crew of people who were calculating, and he figured out how to flow the work from one computer to another. All that kind of stuff. As computing technology started to evolve, he followed that. In the 1970s, a particle physicist like Feynman, that’s my background too, got really interested in using computers to study the properties of elementary particles like the quarks inside a nucleus, you know? We know a proton isn’t really a fundamental object. It’s got little beans rattling around inside, but they’re quantum beans. Gell-Mann, who’s good at names, called them quarks.

John Preskill [00:02:17] – Now we’ve had a theory since the 1970s of how quarks behave, and so in principle, you know everything about the theory, you can compute everything, but you can’t because it’s just too hard. People started to simulate that physics with digital computers in the ’70s, and there were some things that they could successfully compute, and some things they couldn’t because it was just too hard. The resources required, the memory, the time were out of reach. Feynman, in the early ’80s said nature is quantum mechanical damn it, so if you want a simulation of nature, it should be quantum mechanical. You should use a quantum system to behave like another quantum system. At the time, he called it a universal quantum simulator.

John Preskill [00:03:02] – Now we call it a quantum computer. The idea caught on about 10 years later when Peter Shor made the suggestion that we could solve problems which don’t seem to have anything to do with physics, which are really things about numbers like finding the prime factors of a big integer. That caused a lot of excitement,  in part because the implications for cryptography are a big disturbing. But then physicists — good physicists — started to consider, can we really build this thing? Some concluded and argued fairly cogently that no, you couldn’t because of this difficulty that it’s so hard to isolate systems from the environment well enough for them to behave quantumly. It took a few years for that to sort out at the theoretical level. In the mid ’90s we developed a theory called quantum error correction. It’s about how to encode the quantum state that you’d like to protect in such a clever way that even if there are some interactions with the environment that you can’t control, it still stays robust.

John Preskill [00:04:17] – At first, that was just kind of a theorist’s fantasy — it was a little too far ahead of the technology. But 20 years later, the technology is catching up, and now this idea of quantum error correction has become something you can do in the lab.

Craig Cannon [00:04:31] – How does quantum error correction work? I’ve seen a bunch of diagrams, so maybe this is difficult to explain, but how would you explain it?

John Preskill [00:04:39] – Well, I would explain it this way. I don’t think I’ve said the word entanglement yet, have I?

Craig Cannon [00:04:43] – Well, I have been checking off all the Bingo words yet.

John Preskill [00:04:45] – Okay, so let’s talk about entanglement because it’s part of the answer to your question, which I’m still not done answering, what is quantum physics? What do we mean by entanglement? It’s really the characteristic way, maybe the most important way that we know in which quantum is different from ordinary stuff, from classical. Now what does it mean, entanglement? It means that you can have a physical system which has many parts, which have interacted with one another, so it’s in kind of a complex correlated state of all those parts, and when you look at the parts one at a time it doesn’t tell you anything about the state of the whole thing. The whole thing’s in some definite state — there’s information stored in it — and now you’d like to access that information … Let me be a little more concrete. Suppose it’s a book.

John Preskill [00:05:40] – Okay? It’s a book, it’s 100 pages long. If it’s an ordinary book, 100 people could each take a page, and read it, they know what’s on that page, and then they could get together and talk, and now they’d know everything that’s in the book, right? But if it’s a quantum book written in qubits where these pages are very highly entangled, there’s still a lot of information in the book, but you can’t read it the way I just described. You can look at the pages one at a time, but a single page when you look at it just gives you random gibberish. It doesn’t reveal anything about the content of the book. Why is that? There’s information in the book, but it’s not stored in the individual pages. It’s encoded almost entirely in how those pages are correlated with one another. That’s what we mean by quantum entanglement: Information stored in those correlations which you can’t see when you look at the parts one at a time. You asked about quantum error correction?

John Preskill [00:06:39] – What’s the basic idea? It’s to take advantage of that property of entanglement. Because let’s say you have a system of many particles. The environment is kind of kicking them around, it’s interacting with them. You can’t really completely turn off those interactions no matter how hard you try, but suppose we’ve encoded the information in entanglement. So, say, if you look at one atom, it’s not telling you anything about the information you’re trying to protect. The environment isn’t learning anything when it looks at the atoms one at a time.

John Preskill [00:07:15] – This is kind of the key thing — that what makes quantum information so fragile is that when you look at it, you disturb it. This ordinary water bottle isn’t like that. Let’s say we knew it was either here or here, and we didn’t know. I would look at it, I’d find out it’s here. I was ignorant of where it was to start with, and now I know. With a quantum system, when you look at it, you really change the state. There’s no way to avoid that. So if the environment is looking at it in the sense that information is leaking out to the environment, that’s going to mess it up. We have to encode the information so the environment, so to speak, can’t find out anything about what the information is, and that’s the idea of quantum error correction. If we encode it in entanglement, the environment is looking at the parts one at a time, but it doesn’t find out what the protected information is.

Craig Cannon [00:08:06] – In other words, it’s kind of measuring probability the whole way along, right?

John Preskill [00:08:12] – I’m not sure what you mean by that.

Craig Cannon [00:08:15] – Is it Grover’s algorithm that was as quantum bits roll through, go through gates– The probability is determined of what information’s being passed through? What’s being computed?

John Preskill [00:08:30] – Grover’s algorithm is a way of sort of doing an exhaustive search through many possibilities. Let’s say I’m trying to solve some problem like a famous one is the traveling salesman problem. I’ve told you what the distances are between all the pairs of cities, and now I want to find the shortest route I can that visits them all. That’s a really hard problem. It’s still hard for a quantum computer, but not quite as hard because there’s a way of solving it, which is to try all the different routes, and measure how long they are, and then find the one that’s shortest, and you’ve solved the problem. The reason it’s so hard to solve is there’s such a vast number of possible routes. Now what Grover’s algorithm does is it speeds up that exhaustive search.

John Preskill [00:09:29] – In practice, it’s not that big a deal. What it means is that if you had the same processing speed, you can handle about twice as many cities before the problem becomes too hard to solve, as you could if you were using a classical processor. As far as what’s quantum about Grover, it takes advantage of the property in quantum physics that probabilities … tell me if I’m getting too inside baseball …

Craig Cannon [00:10:03] – No, no, this is perfect.

John Preskill [00:10:05] – That probabilities are the squares of amplitudes. This is interference. Again, this is another part of the answer. Well, we can spend the whole hour answering the question, what is quantum physics? Another essential part of it is what we call interference, and this is really crucial for understanding how quantum computing works. That is that probabilities add. If you know the probability of one alternative, and you know the probability of another, then you can add those together and find the probability that one or the other occurred. It’s not like that in quantum physics. The famous example is the double slit interference experiment. I’m sending electrons, let’s say — it could be basketballs, but it’s an easier experiment to do with electrons —

John Preskill [00:11:02] – at a screen, and there are two holes in the screen. You can try to detect the electron on the other side of the screen, and when you do that experiment many times, you can plot a graph showing where the electron was detected in each run, or make a histogram of all the different outcomes. And the graph wiggles, okay? If you could say there’s some probability of going through the first hole, and some probability of going through the second, and each time you detected it, it went through either one or the other, there’d be no wiggles in that graph. It’s the interference that makes it wiggle. The essence of the interference is that nobody can tell you whether it went through the first slit or the second slit. The question is sort of inadmissible. This interference then occurs when we can add up these different alternatives in a way which is different from what we’re used to. It’s not right to say that the electron was detected at this point because it had some probability of going through the first hole, and some probability of going through the second

John Preskill [00:12:23] – and we add those probabilities up. That doesn’t give the right answer. The different alternatives can interfere. This is really important for quantum computing because what we’re trying to do is enhance the probability or the time it takes to find the solution to a problem, and this interference can work to our advantage. We want to have, when we’re doing our search, we want to have a higher chance of getting the right answer, and a lower chance of getting the wrong answer. If the different wrong answers can interfere, they can cancel one another out, and that enhances the probability of getting the right answer. Sorry it’s such a long-winded answer, but this is how Grover’s algorithm works.

John Preskill [00:13:17] – It can speed up exhaustive search by taking advantage of that interference phenomenon.

Craig Cannon [00:13:20] – Well this is kind of one of the underlying questions among many of the questions from Twitter. You’ve hit our record for most questions asked. Basically, many people are wondering what quantum computers really will do if and when it becomes a reality that they outperform classical computers. What are they going to be really good at?

John Preskill [00:13:44] – Well, you know what? I’m not really sure. If you look at the history of technology, it would be hubris to expect me to know. It’s a whole different way of dealing with information. Quantum information is not just … a quantum computer is not just a faster way of computing. It deals with information in a completely new way because of this interference phenomenon, because of entanglement that we’ve talked about. We have limited vision when it comes to predicting decades out what the impact will be of an entirely new way of doing things. Information processing, in particular. I mean you know this well. We go back to the 1960s, and people are starting to put a few transistors on a chip. Where is that going to lead? Nobody knew.

Craig Cannon [00:14:44] – Even early days of the internet.

John Preskill [00:14:45] – Yeah, good example.

Craig Cannon [00:14:46] – Even the first browser. No one really knew what anyone was going to do with it. It makes total sense.

John Preskill [00:14:52] – For good or ill. Yeah. But we have some ideas, you know? I think … why are we confident there will be some transformative effect on society? Of the things we know about, and I emphasize again, probably the most important ones are things we haven’t thought of when it comes to applications of quantum computing, the ones which will affect everyday life, I think, are better methods for understanding and inventing new materials, new chemical compounds. Things like that can be really important. If you find a better way of capturing carbon by designing a better catalyst, or you can design pharmaceuticals that have new effects, materials that have unusual properties. These are quantum physics problems because those properties of the molecule or the material really have to do with the underlying quantum behavior of the particles, and we don’t have a good way for solving such problems or predicting that behavior using ordinary digital computers. That’s what a quantum computer is good at. It’s good — but maybe not the only thing it’s good at — one thing it should certainly be good at is telling us quantitatively how quantum systems behave. In the two contexts I just mentioned, there’s little question that there will be practical impact of that.

Craig Cannon [00:16:37] – It’s not just doing the traveling salesman problem through the table of elements for why it can find these compounds.

John Preskill [00:16:49] – No. If it were, that wouldn’t be very efficient.

Craig Cannon [00:16:52] – Exactly.

John Preskill [00:16:53] – Yeah. No, it’s much trickier than that. Like I said, the exhaustive search, though conceptually it’s really interesting that quantum can speed it up because of interference, from a practical point of view it may not be that big a deal. It means that, well like I said, in the same amount of time you can solve an instance which is twice as big of the problem. What we really get excited about are the so-called exponential speed ups. That was why Shor’s algorithm was exciting in 1994, because factoring large numbers was a problem that had been studied by smart people for a long time, and on that basis, the fact that there weren’t any fast ways of solving it was pretty good evidence it’s a hard problem. Actually, we don’t know how to prove that from first principles. Maybe somebody will come along one day and figure out how to solve factoring very fast on a digital computer. It doesn’t seem very likely because people have been trying for so long to solve problems like that, and it’s just intractable with ordinary computers. You could say the same thing about these quantum physics problems. Maybe some brilliant graduate student is going to drop a paper on the arXiv tomorrow which will say, “Here, I solved quantum chemistry, and I can do it on a digital computer.” But we don’t think that’s very likely because we’ve been working pretty hard on these problems for decades and they seem to be really hard. Those cases, like these number theoretic problems,

John Preskill [00:18:40] – which have cryptological implications, and tasks for simulating the behavior of quantum systems, we’re pretty sure those are hard problems classically, and we’re pretty sure quantum computers … I mean we have algorithms that have been proposed, but which we can’t really run currently because our quantum computers aren’t big enough on the scale that’s needed to solve problems people really care about.

Craig Cannon [00:19:09] – Maybe we should jump to one of the questions from Twitter which is related to that. Travis Scholten (@Travis_Sch) asked, what are the most problem pressings in physics, let’s say specifically around quantum computers that you think substantial progress ought to be made in to move the field forward?

John Preskill [00:19:27] – I know Travis. He was an undergrad here. How you doing, Travis? The problems that we need to solve to make quantum computing closer to realization at the level that would solve problems people care about? Well, let’s go over where we are now.

Craig Cannon [00:19:50] – Yeah, definitely.

John Preskill [00:19:51] – People have been working on quantum hardware for 20 years, working hard, and there are a number of different approaches to building the hardware, and nobody really knows which is going to be the best. I think we’re far from collapsing to one approach which everybody agrees has the best long-term prospects for scalability. And so it’s important that a lot of different types of hardware are being pursued. We can come back to what some of the different approaches are later. Where are we now? We think in a couple of years we’ll have devices with about 50 qubits to 100, and we’ll be able to control them pretty well. That’s an interesting range because even though it’s only 50 to 100 qubits, doesn’t sound like that big a deal, but that’s already too many to simulate with a digital computer, even with the most powerful supercomputers today. From that point of view, these relatively small, near-term quantum computers which we’ll be fooling around with over the next five years or so, are doing something that’s kind of super-classical.

John Preskill [00:21:14] – At least, we don’t know how to do exactly the same things with ordinary computers. Now that doesn’t mean they’ll be able to do anything that’s practically important, but we’re going to try. We’re going to try, and there are ideas about things we’ll try out, including baby versions of these problems in chemistry, and materials, and ways of speeding up optimization problems. Nobody knows how well those things are going to work at these small scales. Part of the reason is not just the number of qubits is small, but they’re also not perfect. We can perform elementary operations on pairs of qubits, which we call quantum gates like the gates in ordinary logic. But they have an error rate a little bit below an error every 100 gates. If you have a circuit with 1000 qubits, that’s a lot of noise.

Craig Cannon [00:22:18] – Exactly. Does for instance, 100-qubit quantum computer really mean 100-qubit quantum computer or do you need a certain amount of backup going on?

John Preskill [00:22:29] – In the near term, we’re going to be trying out, and probably we have the best hopes for, kind of hybrid classical-quantum methods with some kind of classical feedback. You try to do something on the quantum computer, you make a measurement that gives you some information, then you change the way you did it a little bit, and try to converge on some better answer. That’s one possible way of addressing optimization that might be faster on a quantum computer. But I just wanted to emphasize that the number of qubits isn’t the only metric. How good they are, and in particular, the reliability of the gates, how well we can perform them … that’s equally important. Anyway, coming back to Travis’ question, there are lots of things that we’d like to be able to do better. But just having much better qubits would be huge, right? If you … more or less, with the technology we have now, you can have a gate error rate of a few parts in 1,000, you know? If you can improve that by orders of magnitude, then obviously, you could run bigger circuits. That would be very enabling.

John Preskill [00:23:58] – Even if you stick with 100 qubits just by having a circuit with more depth, more layers of gates, that increases the range of what you could do. That’s always going to be important. Because, I mean look at how crappy that is. A gate error rate, even if it’s one part in 1,000, that’s pretty lousy compared to if you look at where–

Craig Cannon [00:24:21] – Your phone has a billion transistors in it. Something like that, and 0%–

John Preskill [00:24:27] – You don’t worry about the … it’s gotten to the point where there is some error protection built in at the hardware level in a processor, because I mean, we’re doing these crazy things like going down from the 11 nanometer scale for features on a chip.

Craig Cannon [00:24:45] – How are folks trying to deal with interference right now?

John Preskill [00:24:50] – You mean, what types of devices? Yeah, so that’s interesting too because there are a range of different ways to do it. I mentioned that we could store information, we could make a qubit out of a single atom, for example. That’s one approach. You have to control a whole bunch of atoms and get them to interact with one another. One way of doing that is with what we call trapped ions. That means the atoms have electrical charges. That’s a good thing because then you could control them with electric fields. You could hold them in a trap, and you can isolate them, like I said, in a very high vacuum so they’re not interacting too much with other things in the laboratory, including stray electric and magnetic fields. But that’s not enough because you got to get them to talk to one another. You got to get them to interact. We have this set of desiderata, which are kind of in tension with one another. On the one hand, we want to isolate the qubits very well. On the other hand, we want to control them from the outside and get them to do what we want them to do, and eventually, we want to read them out. You have to be able to read out the result of the computation. But the key thing is the control. You could have two of those qubits in your device interact with one another in a specified way, and to do that very accurately you have to have some kind of bus that gets the two to talk to one another.

John Preskill [00:26:23] – The way they do that in an ion trap is pretty interesting. It’s by using lasers and controlling how the ions vibrate in the trap, and with a laser, kind of excite, wiggles of the ion, and then by determining whether the ions are wiggling or not, you can go address another ion, and that way you can do a two-qubit interaction. You can do that pretty well. Another way is really completely different. What I just described was encoding information at the one atom level. But another way is to use superconductivity — circuits in which electric current flows without any dissipation. In that case, you have a lot of freedom to sort of engineer the circuits to behave in a quantum way. There are many nuances there, but the key thing is that you can encode information now in a system that might involve the collective motion of billions of electrons, and yet you can control it as though it were a single atom. I mean, here’s one oversimplified way of thinking about it.

John Preskill [00:27:42] – Suppose you have a little loop of wire, and there’s current flowing in the loop. It’s a superconducting wire so it just keeps flowing. Normally, there’d be resistance, which would dissipate that as heat, but not for the superconducting circuit, which of course, has to be kept very cold so it stays superconducting. But you can imagine in this little loop that the current is either circulating clockwise or counterclockwise. That’s a way of encoding information. It could also be both at once, and that’s what makes it a qubit.

Craig Cannon [00:28:14] – Right.

John Preskill [00:28:15] – And so in that case, even though it involves lots of particles, the magic is that you can control that system extremely well. I mentioned individual electrons. That’s another approach. Put the qubit in the spin of a single electron.

Craig Cannon [00:28:32] – You also mentioned better qubits. What did you mean by that?

John Preskill [00:28:35] – Well, what I really care about is how well I can do the gates. There’s a whole other approach, which is motivated by the desire to have much, much better control over the quantum information than we do in those systems that I mentioned so far, superconducting circuits and trapped ions. That’s actually what Microsoft is pushing very hard. We call it topological quantum computing. Topological is a word physicists and mathematicians love. It means, well, we’ll come back to what it means. Anyway, let me just tell you what they’re trying to do. They’re trying to make a much, much better qubit, which they can control much, much better using a completely different hardware approach.

Craig Cannon [00:29:30] – Okay.

John Preskill [00:29:32] – It’s very ambitious because at this point, it’s not even clear they have a single qubit, but if that approach is successful, and it’s making progress, we will see a validated qubit of this type soon. Maybe next year. Nobody really knows where it goes from there, but suppose it’s the case that you could do a two-qubit gate with an error rate of one in a million instead of one in 1,000. That would be huge. Now, scaling all these technologies up, is really challenging from a number of perspectives, including just the control engineering.

Craig Cannon [00:30:17] – How are they doing it or attempting to do it?

John Preskill [00:30:21] – You know, you could ask, where did all this progress come from over 20 years, or so? For example, with the superconducting circuits, a sort of crucial measure is what we call the coherence time of the qubit, which roughly speaking, means how much it interacts with the outside world. The longer the coherence time, the better. The rate of what we call decoherence is essentially how much it’s getting buffeted around by outside influences. For the superconducting circuits, those coherence times have increased about a factor of 10 every three years, going back 15 years or so.

Craig Cannon [00:31:06] – Wow.

John Preskill [00:31:07] – Now, it won’t necessarily go on like that indefinitely, but in order to achieve that type of progress, better materials, better fabrication, better control. The way you control these things is with microwave circuitry. Not that different from the kind of things that are going on in communication devices. All those things are important, but going forward, the control is really the critical thing. Coherence times are already getting pretty long, I mean having them longer is certainly good. But the key thing is to get two qubits to interact just the way you want them to. Even if there is, now I keep saying the key thing is the environment, it’s not the only key thing, right? Because you have some qubit, like if you think about that electron spin, one way of saying it is I said it can be both up and down at the same time. Well, there’s a simpler way of saying that. It might not point either up or down. It might point some other way. But there really are a continuum of ways it could point. That’s not like a bit. See, it’s much easier to stabilize a bit because it’s got two states.

John Preskill [00:32:31] – But if it can kind of wander around in the space of possible configurations for a qubit, that makes it much harder to control. People have gotten better at that, a lot better at that in the last few years.

Craig Cannon [00:32:44] – Interesting. Joshua Harmon asked, what engineering strategy for quantum computers do you think has the most promise?

John Preskill [00:32:53] – Yeah, so I mentioned some of these different approaches, and I guess I’ll interpret the question as, which one is the winning horse? I know better than to answer that question! They’re all interesting. For the near term, the most advanced are superconducting circuits and trapped ions, which is why I mentioned those first. I think that will remain true over the next five to 10 years. Other technologies have the potential — like these topologically protected qubits — to surpass those, but it’s not going to happen real soon. I kind of like superconducting circuits because there’s so much phase space of things you can do with them. Of ways you can engineer and configure them, and imagine scaling them up.

John Preskill [00:33:54] – They have the advantage of being faster. The cycle time, time to do a gate, is faster than with the trapped ions. Just the basic physics of the interactions is different. In the long term, those electron spins could catapult ahead of these other things. That’s something that you can naturally do in silicon, and it’s potentially easy to integrate with silicon technology. Right now, the qubits and gates aren’t as good as the other technologies, but that can change. I mean, from a theorist’s perspective, this topological approach is very appealing. We can imagine it takes off maybe 10 years from now and it becomes the leader. I think it’s important to emphasize we don’t really know what’s going to scale the best.

Craig Cannon [00:34:50] – Right. And are there multiple attempts being made around programming quantum computers?

John Preskill [00:34:55] – Yeah. I mean, some of these companies– That are working on quantum technology now, which includes well-known big players like IBM, and Google, and Microsoft and Intel, but also a lot of startups now. They are trying to encompass the full stack, so they’re interested in the hardware, and the fabrication, and the control technology. But also, the software, the applications, the user interface. All those things are certainly going to be important eventually.

Craig Cannon [00:35:38] – Yeah, they’re pushing it almost to like an AWS layer. Where you interact with your quantum computer in a server farm and you don’t even touch it.

John Preskill [00:35:49] – That’s how it will be in the near term. You’re not going to have, most of us won’t, have a quantum computer sitting on your desktop, or in your pocket. Maybe someday. In the near term, it’ll be in the Cloud, and you’ll be able to run applications on it by some kind of web interface. Ideally, that should be designed so the user doesn’t have to know anything about quantum physics in order to program or use it, and I think that’s part of what some of these companies are moving toward.

Craig Cannon [00:36:24] – Do you think it will get to the level where it’s in your pocket? How do you deal with that when you’re below one kelvin?

John Preskill [00:36:32] – Well, if it’s in your pocket, it probably won’t be one kelvin.

Craig Cannon [00:36:35] – Yeah, probably not.

John Preskill [00:36:38] – What do you do? Well, there’s one approach, as an example, which I guess I mentioned in passing before, where maybe it doesn’t have to be at such low temperature, and that’s nuclear spins. Because they’re very weakly interacting with the outside world, you can have quantum information in a nuclear spin, which — I’m not saying that it would be undisturbed for years, but seconds, which is pretty good. And you can imagine that getting significantly longer. Someday you might have a little quantum smart card in your pocket. The nice thing about that particular technology is you could do it at room temperature. Still have long coherence times. If you go to the ATM and you’re worried that there’s a rogue bank that’s going to steal your information, one solution to that problem — I’m not saying there aren’t other solutions — is to have a quantum card where the bank will be able to authenticate it without being able to forge it.

Craig Cannon [00:37:54] – We should talk about the security element. Kevin Su asked what risk would quantum computers pose to current encryption schemes? So public key, and what changes should people be thinking about if quantum computers come in the next five years, 10 years?

John Preskill [00:38:12] – Yeah. Quantum computers threaten those systems that are in widespread use. Whenever you’re using a web browser and you see that little padlock and you’re at an HTTPS site, you’re using a public key cryptosystem to protect your privacy. Those cryptosystems rely for their security on the presumed hardness of computational problems. That is, it’s possible to crack them, but it’s just too hard. RSA, which is one of the ones that’s widely used … as typically practiced today, to break it you’d have to do something like factor a number which is over 2000 bits long, 2048. That’s too hard to do now. But that’s what quantum computers will be good at. Another one that’s widely used is called elliptic curve cryptography. Doesn’t really matter exactly what it is.

John Preskill [00:39:24] – But the point is that it’s also vulnerable to quantum attack, so we’re going to have to protect our privacy in different ways when quantum computers are prevalent.

Craig Cannon [00:39:37] – What are the attempts being made right now?

John Preskill [00:39:39] – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers.

Craig Cannon [00:39:59] – There you go.

John Preskill [00:40:02] – It turns out that what has sort of become the standard way doesn’t have that feature, and there are alternatives that people are working on. We speak of post-quantum cryptography, meaning the protocols that we’ll have to use when we’re worried that our adversaries have quantum computers. I don’t think there’s any proposed cryptosystem — although there’s a long list of them by now which people think are candidates for being quantum resistant, for being unbreakable, or hard to break by quantum computers. I don’t think there’s any one that the world has sufficient confidence in now that’s really hard for a quantum adversary that we’re all going to switch over. But it’s certainly time to be thinking about it. When people worry about their privacy, of course different users have different standards, but the US Government sometimes says they would like a system to stay secure for 50 years. They’d like to be able to use it for 20, roughly speaking, and then have the intercepted traffic be protected for another 30 after that. I don’t think, though I could be wrong, that we’re likely to have quantum computers that can break those public key cryptosystems in 10 years, but in 50 years seems not unlikely,

John Preskill [00:41:33] – and so we should really be worrying about it. The other one is actually using quantum communication for privacy. In other words, if you and I could send qubits to one another instead of bits, it opens up new possibilities. The way to think about these public key schemes — or one way — that we’re using now, is I want you to send me a private message, and I can send you a lockbox. It has a padlock on it, but I keep the key, okay? But you can close up the box and send it to me. But I’m the only one with the key. The key thing is that if you have the padlock you can’t reverse engineer the key. Of course, it’s a digital box and key, but that’s the idea of public key. The idea of what we call quantum key distribution, which is a particular type of quantum cryptography, is that I can actually send you the key, or you can send me your key, but why can’t any eavesdropper then listen in and know the key? Well it’s because it’s quantum, and remember, it has that property that if you look at it, you disturb it.

John Preskill [00:42:59] – So if you collect information about my key, or if the adversary does, that will cause some change in the key, and there are ways in which we can check whether what you received is really what I sent. And if it turns out it’s not, or it has too many errors in it, then we’ll be suspicious that there was an adversary who tampered with it, and then we won’t use that key. Because we haven’t used it yet — we’re just trying to establish the key. We do the test to see whether an adversary interfered. If it passes the test, then we can use the key. And if it fails the test, we throw that key away and we try again. That’s how quantum cryptography works, but it requires a much different infrastructure than what we’re using now. We have to be able to send qubits … well, it’s not completely different because you can do it with photons. Of course, that’s how we communicate through optical fiber now — we’re sending photons. It’s a little trickier sending quantum information through an optical fiber, because of that issue that interactions with the environment can disturb it. But nowadays, you can send quantum information through an optical fiber over tens of kilometers with a low enough error rate so it’s useful for communication.

Craig Cannon [00:44:22] – Wow.

John Preskill [00:44:23] – Of course, we’d like to be able to scale that up to global distances.

Craig Cannon [00:44:26] – Sure.

John Preskill [00:44:27] – And there are big challenges in that. But anyway, so that’s another approach to the future of privacy that people are interested in.

Craig Cannon [00:44:35] – Does that necessitate quantum computers on both ends?

John Preskill [00:44:38] – Yes, but not huge ones. The reason … well, yes and no. At the scale of tens of kilometers, no. You can do that now. There are prototype systems that are in existence. But if you really want to scale it up —  in other words, to send things longer distance — then you have to bring this quantum error correction idea into the game.

John Preskill [00:45:10] – Because at least with our current photonics technology, there’s no way I can send a single photon from here to China without there being a very high probability that it gets lost in the fiber somewhere. We have to have what we call quantum repeaters, which can boost the signal. But it’s not like the usual type of repeater that we have in communication networks now. The usual type is you measure the signal, and then you resend it. That won’t work for quantum because as soon as you measure it you’re going to mess it up. You have to find a way of boosting it without knowing what it is. Of course, it’s important that it works that way because otherwise, the adversary could just intercept it and resend it. And so it will require some quantum processing to get that quantum error correction in the quantum repeater to work. But it’s a much more modest scale quantum processor than we would need to solve hard problems.

Craig Cannon [00:46:14] – Okay. Gotcha. What are the other things you’re both excited about, and worried about for potential business opportunities? Snehan, I’m mispronouncing names all the times, Snehan Kekre asks, budding entrepreneurs, what should they be thinking about in the context of quantum computing?

John Preskill [00:46:37] – There’s more to quantum technology than computing. Something which has good potential to have an impact in the relatively near future is improved sensing. Quantum systems, partly because of that property that I keep emphasizing that they can’t be perfectly isolated from the outside, they’re good at sensing things. Sometimes, you want to detect it when something in the outside world messes around with your qubit. Again, using this technology of nuclear spins, which I mentioned you can do at room temperature potentially, you can make a pretty good sensor, and it can potentially achieve higher sensitivity and spatial resolution, look at things on shorter distance scales than other existing sensing technology. One of the things people are excited about are the biological and medical implications of that.

John Preskill [00:47:53] – If you can monitor the behavior of molecular machines, probe biological systems at the molecular level using very powerful sensors, that would surely have a lot of applications. One interesting question you can ask is, can you use these quantum error correction ideas to make those sensors even more powerful? That’s another area of current basic research, where you could see significant potential economic impact.

Craig Cannon [00:48:29] – Interesting. In terms of your research right now, what are you working on that you find both interesting and incredibly difficult?

John Preskill [00:48:40] – Everything I work on–

Craig Cannon [00:48:41] – 100%.

John Preskill [00:48:42] – Is both interesting and incredibly difficult. Well, let me change direction a little from what we’ve been talking about so far. Well, I’m going to tell you a little bit about me.

Craig Cannon [00:48:58] – Sure.

John Preskill [00:49:00] – I didn’t start out interested in information in my career. I’m a physicist. I was trained as an elementary particle theorist, studying the fundamental interactions and the elementary particles. That drew me into an interest in gravitation because one thing that we still have a very poor understanding of is how gravity fits together with the other fundamental interactions. The way physicists usually say it is we don’t have a quantum theory of gravity, at least not one that we think is complete and satisfactory. I’ve been interested in that question for many decades, and then got sidetracked because I got excited about quantum computing. But you know what? I’ve always looked at quantum information not just as a technology. I’m a physicist, I’m not an engineer. I’m not trying to build a better computer, necessarily, though that’s very exciting, and worth doing, and if my work can contribute to that, that’s very pleasing. I see quantum information as a new frontier in the exploration of the physical sciences. Sometimes I call it the entanglement frontier. Physicists, we like to talk about frontiers, and stuff. Short distance frontier. That’s what we’re doing at CERN in the Large Hadron Collider, trying to discern new properties of matter at distances which are shorter than we’ve ever been able to explore before.

John Preskill [00:50:57] – There’s a long distance frontier in cosmology. We’re trying to look deeper into the universe and understand its structure and behavior at earlier times. Those are both very exciting frontiers. This entanglement frontier is increasingly going to be at the forefront of basic physics research in the 21st century. By entanglement frontier, I just mean scaling up quantum systems to larger and larger complexity where it becomes harder and harder to simulate those systems with our existing digital tools. That means we can’t very well anticipate the types of behavior that we’re going to see. That’s a great opportunity for new discovery, and that’s part of what’s going to be exciting even in the relatively near term. When we have 100 qubits … there are some things that we can do to understand the behavior of the dynamics of a highly complex system of 100 qubits that we’ve never been able to experimentally probe before. That’s going to be very interesting. But what we’re starting to see now is that these quantum information ideas are connecting to these fundamental questions about gravitation, and how to think about it quantumly. And it turns out, as is true for most of the broader implications of quantum physics, the key thing is entanglement.

John Preskill [00:52:36] – We can think of the microscopic structure of spacetime, the geometry of where we live. Geometry just means who’s close to who else. If we’re in the auditorium, and I’m in the first row and you’re in the fourth row, the geometry is how close we are to one another. Of course, that’s very fundamental in both space and time. How far apart are we in space? How far apart are we in time? Is geometry really a fundamental thing, or is it something that’s kind of emergent from some even more fundamental concept? It seems increasingly likely that it’s really an emergent property.

John Preskill [00:53:29] – That there’s something deeper than geometry. What is it? We think it’s quantum entanglement. That you can think of the geometry as arising from quantum correlations among parts of a system. That’s really what defines who’s close to who. We’re trying to explore that idea more deeply, and one of the things that comes in is the idea of quantum error correction. Remember the whole idea of quantum error correction was that we could make a quantum system behave the way we want it to because it’s well-protected against the damaging effects of noise. It seems like quantum error correction is part of the deep secret of how spacetime geometry works. It has a kind of intrinsic robustness coming from these ideas of quantum error correction that makes space meaningful, so that it doesn’t just evaporate when you tap on it. If you wanted to, you could think of the spacetime, the space that you’re in and the space that I’m in, as parts of a system that are entangled with one another.

John Preskill [00:54:45] – What would happen if we broke that entanglement and your part of space became disentangled from my part? Well what we think that would mean is that there’d be no way to connect us anymore. There wouldn’t be any path through space that starts over here with me and ends with you. It’d become broken apart into two pieces. It’s really the entanglement which holds space together, which keeps it from falling apart into little pieces. We’re trying to get a deeper grasp of what that means.

Craig Cannon [00:55:19] – How do you make any progress on that? That seems like the most unbelievably difficult problem to work on.

John Preskill [00:55:26] – It’s difficult because, well for a number of reasons, but in particular, because it’s hard to get guidance from experiment, which is how physics historically–

Craig Cannon [00:55:38] – All science.

John Preskill [00:55:38] – Has advanced.

Craig Cannon [00:55:39] – Yeah.

John Preskill [00:55:41] – Although it was fun a moment ago to talk about what would happen if we disentangled your part of space from mine, I don’t know how to do that in the lab right now. Of course, part of the reason is we have the audacity to think we can figure these things out just by thinking about them. Maybe that’s not true. Nobody knows, right? We should try. Solving these problems is a great challenge, and it may be that the apes that evolved on Earth don’t have the capacity to understand things like the quantum structure of spacetime. But maybe we do, so we should try. Now in the longer term, and maybe not such a long term, maybe we can get some guidance from experiment. In particular, what we’re going to be doing with quantum computers and the other quantum technologies that are becoming increasingly sophisticated in the next couple of decades, is we’ll be able to control very well highly entangled complex quantum systems. That should mean that in a laboratory, on a tabletop, I can sort of make my own little toy space time …

John Preskill [00:57:02] – with an emergent geometry arising from the properties of that entanglement, and I think that’ll teach us lessons because systems like that are the types of system that, because they’re so highly entangled, digital computers can’t simulate them. It seems like only quantum computers are potentially up to the task. So that won’t be quite the same as disentangling your side of the room from mine, in real life. But we’d be able to do it in a laboratory setting using model systems, which I think would help us to understand the basic principles better.

Craig Cannon [00:57:39] – Wild. Yeah, desktop space time seems pretty cool, if you could figure it out.

John Preskill [00:57:43] – Yeah, it’s pretty fundamental. We didn’t really talk about what people sometimes, we did implicitly, but not in so many words. We didn’t talk about what people sometimes call quantum non-locality. It’s another way of describing quantum entanglement, actually. There’s this notion of Bell’s theorem that when you look at the correlations among the parts of a quantum system, that they’re different from any possible classical correlations. Some things that you read give you the impression that you can use that to instantaneously send information over long distances. It is true that if we have two qubits, electron spins, say, and they’re entangled with one another, then what’s kind of remarkable is that I can measure my qubit to see along some axis whether it’s up or down, and you can measure yours, and we will get perfectly correlated results. When I see up, you’ll see up, say, and when I see down, you’ll see down. And sometimes, people make it sound like that’s remarkable. That’s not remarkable in itself. Somebody could’ve flipped a pair of coins, you know,

John Preskill [00:59:17] – so that they came up both heads or both tails, and given one to you and one –

Craig Cannon [00:59:20] – Split them apart.

John Preskill [00:59:20] – to me.

Craig Cannon [00:59:21] – Yeah.

John Preskill [00:59:22] – And gone a light year apart, and then we both …  hey, mine’s heads. Mine’s heads too!

Craig Cannon [00:59:24] – And then they call it quantum teleportation on YouTube.

John Preskill [00:59:28] – Yeah. Of course, what’s really important about entanglement that makes it different from just those coins is that there’s more than one way of looking at a qubit. We have what we call complementary ways of measuring it, so you can ask whether it’s up or down along this axis or along that axis. There’s nothing like that for the coins. There’s just one way to look at it. What’s cool about entanglement is that we’ll get perfectly correlated results if we both measure in the same way, but there’s more than one possible way that we could measure. What sometimes gets said, or the impression people get, is that that means that when I do something to my qubit, it instantaneously affects your qubit, even if we’re on different sides of the galaxy. But that’s not what entanglement does. It just means they’re correlated in a certain way.

John Preskill [01:00:30] – When you look at yours, if we have maximally entangled qubits, you just see a random bit. It could be a zero or a one, each occurring with probability 1/2. That’s going to be true no matter what I did to my qubit, and so you can’t tell what I did by just looking at it. It’s only that if we compared notes later we can see how they’re correlated, and that correlation holds for either one of these two complementary ways in which we could both measure. It’s that fact that we have these complementary ways to measure that makes it impossible for a classical system to reproduce those same correlations. So that’s one misconception that’s pretty widespread. Another one is this about quantum computing, which is in trying to explain why quantum computers are powerful, people will sometimes say, well, it’s because you can superpose –I used that word before, you can add together many different possibilities. That means that, whereas an ordinary computer would just do a computation once, acting on a superposition a quantum computer can do a vast number of computations all at once.

John Preskill [01:01:54] – There’s a certain sense in which that’s mathematically true if you interpret it right, but it’s very misleading. Because in the end, you’re going to have to make some measurement to read out the result. When you read it out, there’s a limited amount of information you can get. You’re not going to be able to read out the results of some huge number of computations in a single shot measurement. Really the key thing that makes it work is this idea of interference, which we discussed briefly when you asked about Grover’s algorithm. The art of a quantum algorithm is to make sure that the wrong answers interfere and cancel one another out, so the right answer is enhanced. That’s not automatic. It requires that the quantum algorithm be designed in just the right way.

Craig Cannon [01:02:50] – Right. The diagrams I’ve seen online at least, involve usually you’re squaring the output as it goes along, and then essentially, that flips the correct answer to the positive, and the others are in the negative position. Is that accurate?

John Preskill [01:03:08] – I wouldn’t have said it the way you did– Because you can’t really measure it as you go along. Once you measure it, the magic of superposition is going to be lost.

John Preskill [01:03:19] – It means that now there’s some definite outcome or state. To take advantage of this interference phenomenon, you need to delay the measurement. Remember when we were talking about the double slit and I said, if you actually see these wiggles in the probability of detection, which is the signal of interference, that means that there’s no way anybody could know whether the electron went through hole one or hole two? It’s the same way with quantum computing. If you think of the computation as being a superposition of different possible computations, it wouldn’t work — there wouldn’t be a speed up — if you could know which of those paths the computation followed. It’s important that you don’t know. And so you have to sum up all the different computations, and that’s how the interference phenomenon comes into play.

Craig Cannon [01:04:17] – To take a little sidetrack, you mentioned Feynman before. And before we started recording you mentioned working with him. I know I’m in the Feynman fan club, for sure. What was that experience like?

John Preskill [01:04:32] – We never really collaborated. I mean, we didn’t write a paper together, or anything like that. We overlapped for five years at Caltech. I arrived here in 1983. He died in 1988. We had offices on the same corridor, and we talked pretty often because we were both interested in the fundamental interactions, and in particular, what we call quantum chromodynamics. It’s our theory of how nuclear matter behaves, how quarks interact, what holds the proton together, those kinds of things. One big question is what does hold the proton together? Why don’t the quarks just fall apart? That was an example of a problem that both he and I were very interested in, and which we talked about sometimes. Now, this was pretty late in his career. When I think about it now, when I arrived at Caltech, that was 1983, Feynman was born in 1918, so he was 65. I’m 64 now, so maybe he wasn’t so old, right? But at the time, he seemed pretty ancient to me. Since I was 30.

John Preskill [01:05:58] – Those who interacted with Dick Feynman when he was really at his intellectual peak in the ’40s, and ’50s, and ’60s, probably saw even more extraordinary intellectual feats than I witnessed interacting with the 65 year old Feynman. He just loved physics, you know? He just thought everything was so much fun. He loved talking about it. He wasn’t as good a listener as a talker, but actually – well that’s a little unfair, isn’t it? It was kind of funny because Feynman, he always wanted to think things through for himself, sort of from first principles, rather than rely on the guidance from experts who have thought about these things before. Well that’s fine. You should try to understand things as deeply as you can on your own, and sort of reconstruct the knowledge from the ground up. That’s very enabling, and gives you new insights. But he was a little too dismissive, in my view, of what the other guys knew. But I could slip it in because I didn’t tell him, “Dick, you should read this paper by Polyakov” — well maybe I did, but he wouldn’t have even heard that  — because he solved that problem that you’re talking about.

John Preskill [01:07:39] – But I knew what Polyakov had said about it, so I would say, “Oh well, look, why don’t we look at it this way?” And so he thought I was, that I was having all these insights, but the truth was the big difference between Feynman and me in the mid 1980s was I was reading literature, and he wasn’t.

Craig Cannon [01:08:00] – That’s funny.

John Preskill [01:08:01] – Probably, if he had been, he would’ve been well served, but that wasn’t the way he liked to work on things. He wanted to find his own approach. Of course, that had worked out pretty well for him throughout his career.

Craig Cannon [01:08:15] – What other qualities did you notice about him when he was roaming the corridors?

John Preskill [01:08:21] – He’d always be drumming. So you would know he was around because he’d actually be walking down the hallway drumming on the wall.

Craig Cannon [01:08:27] – Wait, with his hands, or with sticks, or–

John Preskill [01:08:29] – No, hands. He’d just be tapping.

Craig Cannon [01:08:32] – Just a bongo thing.

John Preskill [01:08:33] – Yeah. That was one thing. He loved to tell stories. You’ve probably read the books that Ralph Leighton put together based on the stories Feynman told. Ralph did an amazing job, of capturing Feynman’s personality in writing those stories down because I’d heard a lot of them. I’m sure he told the same stories to many people many times, because he loved telling stories. But the book really captures his voice pretty well.

John Preskill [01:09:12] – If you had heard him tell some of these stories, and then you read the way Ralph Leighton transcribed them, you can hear Feynman talking. At the time that I knew him, one of the experiences that he went through was he was on the Challenger commission after the space shuttle blew up. He was in Washington a lot of the time, but he’d come back from time to time, and he would sort of sit back and relax in our seminar room and start bringing us up to date on all the weird things that were happening on the Challenger commission. That was pretty fun.

Craig Cannon [01:09:56] – That’s really cool.

John Preskill [01:09:56] – A lot of that got captured in the second volume. I guess it’s the one called, What Do You Care What Other People Think? There’s a chapter about him telling stories about the Challenger commission. He was interested in everything. It wasn’t just physics. He was very interested in biology. He was interested in computation. I remember how excited he was when he got his first IBM PC. Probably not long after I got to Caltech. Yeah, it was what they called the AT. We thought it was a pretty sexy machine. I had one, too. He couldn’t wait to start programming it in BASIC.

Craig Cannon [01:10:50] – Very cool.

John Preskill [01:10:51] – Because that was so much fun.

Craig Cannon [01:10:52] – There was a question that I was kind of curious to your answer. Tika asks about essentially, teaching about quantum computers. They say, many kids in grade 10 can code. Some can play with machine learning tools without knowing the math. Can quantum computing become as simple and/or accessible?

John Preskill [01:11:17] – Maybe so. At some level, when people say quantum mechanics is counterintuitive, it’s hard for us to grasp, it’s so foreign to our experience, that’s true. The way things behave at the microscopic scale are, like we discussed earlier, really different from the way ordinary stuff behaves. But it’s a question of familiarity. What I wouldn’t be surprised by is that if you go out a few decades, kids who are 10 years old are going to be playing quantum games. That’s an application area that doesn’t get discussed very much, but there could be a real market there because people love games. Quantum games are different, and the strategies are different, and what you have to do to win is different. If you play the game enough, you start to get the hang of it.

John Preskill [01:12:26] – I don’t see any reason why kids who have not necessarily deeply studied physics can’t get a pretty good feel for how quantum mechanics works. You know, the way ordinary physics works, maybe it’s not so intuitive. Newton’s laws … Aristotle couldn’t get it right. He thought you had to keep pushing on something to get it to keep moving. That wasn’t right. Galileo was able to roll balls down a ramp, and things like that, and see he didn’t have to keep pushing to keep it moving. He could see that it was uniformly accelerated in a gravitational field. Newton took that to a much more general and powerful level. You fool around with stuff, and you get the hang of it. And I think quantum stuff can be like that. We’ll experience it in a different way, but when we have quantum computers, in a way, that opens the opportunity for trying things out and seeing what happens.

John Preskill [01:13:50] – After you’ve played the game enough, you start to anticipate. And actually, it’s an important point about the applications. One of the questions you asked me at the beginning was what are we able to do with quantum computers? And I said, I don’t know. So how are we going to discover new applications? It might just be, at least in part, by fooling around. A lot of classical algorithms that people use on today’s computers were discovered, or that they were powerful was discovered, by experimenting. By trying it. I don’t know … what’s an example of that? Well, the simplex method that we use in linear programming. I don’t think there was a mathematical proof that it was fast at first, but people did experiments, and they said, hey, this is pretty fast.

Craig Cannon [01:14:53] – Well, you’re seeing it a lot now in machine learning.

John Preskill [01:14:57] – Yeah, well that’s a good example.

Craig Cannon [01:14:58] – You test it out a million times over when you’re running simulations, and it turns out, that’s what works. Following the thread of education, and maybe your political interest, given it’s the year that it is, do you have thoughts on how you would adjust or change STEM education?

John Preskill [01:15:23] – Well, no particularly original thoughts. But I do think that STEM education … we shouldn’t think of it as we’re going to need this technical workforce, and so we better train them. The key thing is we want the general population to be able to reason effectively, and to recognize when an argument is phony and when it’s authentic. To think about, well how can I check whether what I just read on Facebook is really true? And I see that as part of the goal of STEM education. When you’re teaching kids in school how to understand the world by doing experiments, by looking at the evidence, by reasoning from the evidence, this is something that we apply in everyday life, too. I don’t know exactly how to implement this–

John Preskill [01:16:36] – But I think we should have that perspective that we’re trying to educate a public, which is going to eventually make critical decisions about our democracy, and they should understand how to tell when something is true or not. That’s a hard thing to do in general, but you know what I mean. That there are some things that, if you’re a person with some — I mean it doesn’t necessarily have to be technical — but if you’re used to evaluating evidence and making a judgment based on that evidence about whether it’s a good argument or not, you can apply that to all the things you hear and read, and make better judgments.

Craig Cannon [01:17:23] – What about on the policy side? Let’s see, JJ Francis asked that, if you or any of your colleagues would ever consider running for office. Curious about science policy in the US.

John Preskill [01:17:38] – Well, it would be good if we had more scientifically trained people in government. Very few members of Congress. I know of one, Bill Foster’s a physicist in Illinois. He was a particle physicist, and he worked at Fermilab, and now he’s in Congress, and very interested in the science and educational policy aspects of government. Rush Holt was a congressman from New Jersey who had a background in physics. He retired from the House a couple of years ago, but he was in Congress for something like 18 years, and he had a positive influence, because he had a voice that people respected when it came to science policy. Having more people like that would help. Now, another thing, it doesn’t have to be elective office.

Craig Cannon [01:18:39] – Right.

John Preskill [01:18:42] – There are a lot of technically trained people in government, many of them making their careers in agencies that deal with technical issues. Department of Defense, of course, there are a lot of technical issues. In the Obama Administration we had two successive secretaries of energy who were very, very good physicists. Steve Chu was Nobel Prize winning physicist. Then Ernie Moniz, who’s a real authority on nuclear energy and weapons. That kind of expertise makes a difference in government.

John Preskill [01:19:24] – Now the Secretary of Energy is Rick Perry. It’s a different background.

Craig Cannon [01:19:28] – Yeah, you could say that. Just kind of historical reference, what policies did they put in place that you really felt their hand as a physicist move forward?

John Preskill [01:19:44] – You mean in particular–

Craig Cannon [01:19:45] – I’m talking the Obama Administration.

John Preskill [01:19:49] – Well, I think the Department of Energy, DOE, tried to facilitate technical innovation by seeding new technologies, by supporting startup companies that were trying to do things that would improve battery technology, and solar power, and things like that, which could benefit future generations. They had an impact by doing that. You don’t have to be a Nobel Prize winning physicist to think that’s a good idea. That the administration felt that was a priority made a difference, and appointing a physicist at Department of Energy was, if nothing else, highly symbolic of how important those things are.

Craig Cannon [01:20:52] – On the quantum side, someone asked Vikas Karad, he asked where the Quantum Valley might be. Do you have thoughts, as in Silicon Valley for quantum computing?

John Preskill [01:21:06] – Well… I don’t know, but you look at what’s happening the last couple of years, there have been a number of quantum startups. A notable number of them are in the Bay Area. Why so? Well, that’s where the tech industry is concentrated and where the people who are interested in financing innovative technical startups are concentrated. If you are an entrepreneur interested in starting a company, and you’re concerned about how to fundraise for it, it kind of makes sense to locate in that area. Now, that’s what’s sort of happening now, and may not continue, of course. It might not be like that indefinitely. Nothing lasts forever, but I would say… That’s the place, Silicon Valley is likely to be Quantum Valley, the way things are right now.

Craig Cannon [01:22:10] – Well then what about the physicists who might be listening to this? If they’re thinking about starting a company, do you have advice for them?

John Preskill [01:22:22] – Just speaking very generally, if you’re putting a team together… Different people have different expertise. Take quantum computing as an example, like we were saying earlier, some of the big players and the startups, they want to do everything. They want to build the hardware, figure out better ways to fabricate it. Better control, better software, better applications. Nobody can be an expert on all those things. Of course, you’ll hire a software person to write your software, and microwave engineer to figure out your control, and of course that’s the right thing to do. But I think in that arena, and it probably applies to other entrepreneurial activity relating to physics, being able to communicate across those boundaries is very valuable, and you can see it in quantum computing now. That if the man or woman who’s involved in the software has that background, but there’s not a big communication barrier talking to the people who are doing the control engineering, that can be very helpful. It makes sense to give some preference to the people who maybe are comfortable doing so, or have the background that stretches across more than one of those areas of expertise. That can be very enabling in a technology arena like quantum computing today, where we’re trying to do really, really hard stuff, and you don’t know whether you’ll succeed, and you want to give it your best go by seeing the connections between those different things.

Craig Cannon [01:24:28] – Would you advise someone then to maybe teach or try and explain it to, I don’t know their young cousins? Because Feynman maybe recognizes the king of communicating physics, at least for a certain period of time. How would you advise someone to get better at it so they can be more effective?

John Preskill [01:24:50] – Practice. There are different aspects of that. This isn’t what you meant at all, but I’ll say it anyway, because what you asked brought it to mind. If you teach, you learn. We have this odd model in the research university that a professor like me is supposed to do research and teach. Why don’t we hire teachers and researchers? Why do we have the same people doing both? Well, part of the reason for me is most of what I know, what I’ve learned since my own school education ended, is knowledge I acquired by trying to teach it. To keep our intellect rejuvenated, we have to have that experience of trying to teach new things that we didn’t know that well before to other people. That deepens your knowledge. Just thinking about how you convey it makes you ask questions that you might not think to ask otherwise, and you say “Hey, I don’t know the answer to that.” Then you have to try to figure it out. So I think that applies at varying levels to any situation in which a scientist, or somebody with a technical background, is trying to communicate.

John Preskill [01:26:21] – By thinking about how to get it across to other people, we can get new insights, you know? We can look at it in a different way. It’s not a waste of time. Aside from the benefits of actually successfully communicating, we benefit from it in this other way. But other than that… Have fun with it, you know? Don’t look at it as a burden, or some kind of task you have to do along with all the other things you’re doing. It should be a pleasure. When it’s successful, it’s very gratifying. If you put a lot of thought into how to communicate something and you think people are getting it, that’s one of the ways that somebody in my line of work can get a lot of satisfaction.

Craig Cannon [01:27:23] – If now were to be your opportunity to teach a lot of people about physics, and you could just point someone to things, who would you advise someone to be? They want to learn more about quantum computing, they want to learn about physics. What should they be reading? What YouTube channel should they follow? What should they pay attention to?

John Preskill [01:27:44] – Well one communicator who I have great admiration for is Leonard Susskind, who’s at Stanford. You mentioned Feynman as the great communicator, and that’s fair, but in terms of style and personality of physicists who are currently active, I think Lenny Susskind is the most similar to Feynman of anyone I can think of. He’s a no bullshit kind of guy. He wants to give you the straight stuff. He doesn’t want to water it down for you. But he’s very gifted when it comes to making analogies and creating the illusion that you’re understanding what he’s saying. He has … if you just go to YouTube and search Leonard Susskind you’ll see lectures that he’s given at Stanford where they have some kind of extension school for people who are not Stanford students, people in the community. A lot of them in the tech community because it’s Stanford, and he’s giving courses. Yeah, and on quite sophisticated topics, but also on more basic topics, and he’s in the process of turning those into books. I’m not sure how many of those have appeared, but he has a series called The Theoretical Minimum

John Preskill [01:29:19] – which is supposed to be the gentle introduction to different topics like classical physics, quantum physics, and so on. He’s pretty special I think in his ability to do that.

Craig Cannon [01:29:32] – I need to subscribe. Actually, here’s a question then. In the things you’ve relearned while teaching over the past, I guess it’s 35 years now.

John Preskill [01:29:46] – Shit, is that right?

Craig Cannon [01:29:47] – Something like that.

John Preskill [01:29:48] – That’s true. Yeah.

Craig Cannon [01:29:51] – What were the big thing, what were the revelations?

John Preskill [01:29:55] – That’s how I learned quantum computing, for one thing. I was not at all knowledgeable about information science. That wasn’t my training. Back when I was in school, physicists didn’t learn much about things like information theory, computer science, complexity theory. One of the great things about quantum computing is its interdisciplinary character, that it brings these different things into contact, which traditionally had not been part of the common curriculum of any community of scholars. I decided 20 years ago that I should teach a quantum information class at Caltech, and I worked very hard on it that year. Not that I’m an expert, or anything, but I learned a lot about information theory, and things like channel capacity, and computational complexity — how we classify the hardness of problems — and algorithms. Things like that, which I didn’t really know very well. I had sort of a passing familiarity with some of those things from reading some of the quantum computing literature. That’s no substitute for teaching a class because then you really have to synthesize it and figure out your way of presenting it. Most of the notes are typed up and you can still get to them on my website.That was pretty transformative for me … and it was easier then, 20 years ago, I guess than it is now because it was such a new topic.

John Preskill [01:31:49] – But I really felt I was kind of close enough to the cutting edge on most of those topics by the time I’d finished the class that I wasn’t intimidated by another paper I’d read or a new thing I’d hear about those things. That was probably the one case where it really made a difference in my foundation of knowledge which enabled me to do things. But I had the same experience in particle physics. When I was a student, I read a lot. I was very broadly interested in physics. But when the first time, I was still at Harvard at the time –later I taught a similar course here — I’m in my late 20s, I’m just a year or two out of graduate school, and I decide to teach a very comprehensive class on elementary particles … in particular, quantum chromodynamics, the theory of nuclear forces like we talked about before. It just really expanded my knowledge to have that experience of teaching that class. I still draw on that. I can still remember that experience and I think I get ideas that I might not otherwise have because I went through that.

Craig Cannon [01:33:23] – I want to get involved now. I want to go back to school, or maybe teach a class. I don’t know.

John Preskill [01:33:27] – Well, what’s stopping you?

Craig Cannon [01:33:29] – Nothing. Alright, thanks John.

John Preskill [01:33:32] – Okay, thank you Craig.

# Rock-paper-scissors, granite-clock-idea

I have a soft spot for lamassu. Ten-foot-tall statues of these winged bull-men guarded the entrances to ancient Assyrian palaces. Show me lamassu, or apkallu—human-shaped winged deities—or other reliefs from the Neo-Assyrian capital of Nineveh, and you’ll have trouble showing me the door.

Assyrian art fills a gallery in London’s British Museum. Lamassu flank the gallery’s entrance. Carvings fill the interior: depictions of soldiers attacking, captives trudging, and kings hunting lions. The artwork’s vastness, its endurance, and the contact with a three-thousand-year-old civilization floor me. I tore myself away as the museum closed one Sunday night.

I visited the British Museum the night before visiting Jonathan Oppenheim’s research group at University College London (UCL). Jonathan combines quantum information theory with thermodynamics. He and others co-invented thermodynamic resource theories (TRTs), which Quantum Frontiers regulars will know of. TRTs are quantum-information-theoretic models for systems that exchange energy with their environments.

Energy is conjugate to time: Hamiltonians, mathematical objects that represent energy, represent also translations through time. We measure time with clocks. Little wonder that one can study quantum clocks using a model for energy exchanges.

Mischa Woods, Ralph Silva, and Jonathan used a resource theory to design an autonomous quantum clock. “Autonomous” means that the clock contains all the parts it needs to operate, needs no periodic winding-up, etc. When might we want an autonomous clock? When building quantum devices that operate independently of classical engineers. Or when performing a quantum computation: Computers must perform logical gates at specific times.

Wolfgang Pauli and others studied quantum clocks, the authors recall. How, Pauli asked, would an ideal clock look? Its Hamiltonian, $\hat{H}_{\rm C}$, would have eigenstates $| E \rangle$. The labels $E$ denote possible amounts of energy.

The Hamiltonian would be conjugate to a “time operator” $\hat{t}$. Let $| \theta \rangle$ denote an eigenstate of $\hat{t}$. This “time state” would equal an even superposition over the $| E \rangle$’s. The clock would occupy the state $| \theta \rangle$ at time $t_\theta$.

Imagine measuring the clock, to learn the time, or controlling another system with the clock. The interaction would disturb the clock, changing the clock’s state. The disturbance wouldn’t mar the clock’s timekeeping, if the clock were ideal. What would enable an ideal clock to withstand the disturbances? The ability to have any amount of energy: $E$ must stretch from $- \infty$ to $\infty$. Such clocks can’t exist.

Approximations to them can. Mischa, Ralph, and Jonathan designed a finite-size clock, then characterized how accurately the clock mimics the ideal. (Experts: The clock corresponds to a Hilbert space of finite dimensionality $d$. The clock begins in a Gaussian state that peaks at one time state $| \theta \rangle$. The finite-width Gaussian offers more stability than a clock state.)

Disturbances degrade our ability to distinguish instants by measuring the clock. Imagine gazing at a kitchen clock through blurry lenses: You couldn’t distinguish 6:00 from 5:59 or 6:01. Disturbances also hinder the clock’s ability to implement processes, such as gates in a computation, at desired instants.

Mischa & co. quantified these degradations. The errors made by the clock, they found, decay inverse-exponentially with the clock’s size: Grow the clock a little, and the errors shrink a lot.

Time has degraded the lamassu, but only a little. You can distinguish feathers in their wings and strands in their beards. People portray such artifacts as having “withstood the flow of time,” or “evaded,” or “resisted.” Such portrayals have never appealed to me. I prefer to think of the lamassu as surviving not because they clash with time, but because they harmonize with it. The prospect of harmonizing with time—whatever that means—has enticed me throughout my life. The prospect partially underlies my research into time—perhaps childishly, foolishly—I recognize if I remove my blurry lenses before gazing in the mirror.

The creation of lasting works, like lamassu, has enticed me throughout my life. I’ve scrapbooked, archived, and recorded, and tended memories as though they were Great-Grandma’s cookbook. Ancient civilizations began alluring me at age six, partially due to artifacts’ longevity. No wonder I study the second law of thermodynamics.

Yet doing theoretical physics makes no sense from another perspective. The ancient Egyptians sculpted granite, when they could afford it. Gudea, king of the ancient city-state of Lagash, immortalized himself in diorite. I fashion ideas, which lack substance. Imagine playing, rather than rock-paper-scissors, granite-diorite-idea. The idea wouldn’t stand a chance.

Would it? Because an idea lacks substance, it can manifest in many forms. Plato’s cave allegory has manifested as a story, as classroom lectures, on handwritten pages, on word processors and websites, in cartloads of novels, in the film The Matrix, in one of the four most memorable advertisements I received from colleges as a high-school junior, and elsewhere. Plato’s allegory has survived since about the fourth century BCE. King Ashurbanipal’s lion-hunt reliefs have survived for only about 200 years longer.

The lion-hunt reliefs—and lamassu—exude a grandness, a majesty that’s attracted me as their longevity has. The nature of time and the perfect clock have as much grandness. Leaving the British Museum’s Assyrian gallery at 6 PM one Sunday, I couldn’t have asked for a more fitting location, 24 hours later, than in a theoretical-physics conversation.

With thanks to Jonathan, to Álvaro Martín-Alhambra, and to Mischa for their hospitality at UCL; to Ada Cohen for the “Art history of ancient Egypt and the ancient Near East” course for which I’d been hankering for years; to my brother, for transmitting the ancient-civilizations bug; and to my parents, who fed the infection with museum visits.

Click here for a follow-up to the quantum-clock paper.