Quantum Algorithms: A Call To Action

Posted on April 20, 2025 by robbieking1000

Quantum computing finds itself in a peculiar situation. On the technological side, after billions of dollars and decades of research, working quantum computers are nearing fruition. But still, the number one question asked about quantum computers is the same as it was two decades ago: What are they good for? The honest answer reveals an elephant in the room: We don’t fully know yet. For theorists like me, this is an opportunity, a call to action.

Technological momentum

Suppose we do not have quantum computers in a few decades time. What will be the reason? It’s unlikely that we’ll encounter some insurmountable engineering obstacle. The theoretical basis of quantum error-correction is solid, and several platforms are approaching or below the error-correction threshold (Harvard, Yale, Google). Experimentalists believe today’s technology can scale to 100 logical qubits and $10^6$ gates—the megaquop era. If mankind spends $100 billion over the next few decades, it’s likely we could build a quantum computer.

A more concerning reason that quantum computing might fail is that there is not enough incentive to justify such a large investment in R&D and infrastructure. Let’s make a comparison to nuclear fusion. Like quantum hardware, they have challenging science and engineering problems to solve. However, if a nuclear fusion lab were to succeed in their mission of building a nuclear fusion reactor, the application would be self-evident. This is not the case for quantum computing—it is a sledgehammer looking for nails to hit.

Nevertheless, industry investment in quantum computing is currently accelerating. To maintain the momentum, it is critical to match investment growth and hardware progress with algorithmic capabilities. The time to discover quantum algorithms is now.

Empowered theorists

Theory research is forward-looking and predictive. Theorists such as Geoffrey Hinton laid the foundations of the current AI revolution. But decades later, with an abundance of computing hardware, AI has become much more of an empirical field. I look forward to the day that quantum hardware reaches a state of abundance, but that day is not yet here.

Today, quantum computing is an area where theorists have extraordinary leverage. A few pages of mathematics by Peter Shor inspired thousands of researchers, engineers and investors to join the field. Perhaps another few pages by someone reading this blog will establish a future of world-altering impact for the industry. There are not many places where mathematics has such potential for influence. An entire community of experimentalists, engineers, and businesses are looking to the theorists for ideas.

The Challenge

Traditionally, it is thought that the ideal quantum algorithm would exhibit three features. First, it should be provably correct, giving a guarantee that executing the quantum circuit reliably will achieve the intended outcome. Second, the underlying problem should be classically hard—the output of the quantum algorithm should be computationally hard to replicate with a classical algorithm. Third, it should be useful, with the potential to solve a problem of interest in the real world. Shor’s algorithm comes close to meeting all of these criteria. However, demanding all three in an absolute fashion may be unnecessary and perhaps even counterproductive to progress.

Provable correctness is important, since today we cannot yet empirically test quantum algorithms on hardware at scale. But what degree of evidence should we require for classical hardness? Rigorous proof of classical hardness is currently unattainable without resolving major open problems like P vs NP, but there are softer forms of proof, such as reductions to well-studied classical hardness assumptions.

I argue that we should replace the ideal of provable hardness with a more pragmatic approach: The quantum algorithm should outperform the best known classical algorithm that produces the same output by a super-quadratic speedup.¹ Emphasizing provable classical hardness might inadvertently impede the discovery of new quantum algorithms, since a truly novel quantum algorithm could potentially introduce a new classical hardness assumption that differs fundamentally from established ones. The back-and-forth process of proposing and breaking new assumptions is a productive direction that helps us triangulate where quantum advantage lies.

It may also be unproductive to aim directly at solving existing real-world problems with quantum algorithms. Fundamental computational tasks with quantum advantage are special and we have very few examples, yet they necessarily provide the basis for any eventual quantum application. We should search for more of these fundamental tasks and match them to applications later.

That said, it is important to distinguish between quantum algorithms that could one day provide the basis for a practically relevant computation, and those that will not. In the real world, computations are not useful unless they are verifiable or at least repeatable. For instance, consider a quantum simulation algorithm that computes a physical observable. If two different quantum computers run the simulation and get the same answer, one can be confident that this answer is correct and that it makes a robust prediction about the world. Some problems such as factoring are naturally easy to verify classically, but we can set the bar even lower: The output of a useful quantum algorithm should at least be repeatable by another quantum computer.

There is a subtle fourth requirement of paramount importance that is often overlooked, captured by the following litmus test: If given a quantum computer tomorrow, could you implement your quantum algorithm? In order to do so, you need not only a quantum algorithm but also a distribution over its inputs on which to run it. Classical hardness must then be judged in the average case over this distribution of inputs, rather than in the worst case.

I’ll end this section with a specific caution regarding quantum algorithms whose output is the expectation value of an observable. A common reason these proposals fail to be classically hard is that the expectation value exponentially concentrates over the distribution of inputs. When this happens, a trivial classical algorithm can replicate the quantum result by simply outputting the concentrated (typical) value for every input. To avoid this, we must seek ensembles of quantum circuits whose expectation values exhibit meaningful variation and sensitivity to different inputs.

We can crystallize these priorities into the following challenge:

The Challenge
Find a quantum algorithm and a distribution over its inputs with the following features:
— (Provable correctness.) The quantum algorithm is provably correct.
— (Classical hardness.) The quantum algorithm outperforms the best known classical algorithm that performs the same task by a super-quadratic speedup, in the average-case over the distribution of inputs.
— (Potential utility.) The output is verifiable, or at least repeatable.

Examples and non-examples

Category	Classically verifiable	Quantumly repeatable	Potentially useful	Provable classical hardness	Examples
Search problem	Yes	Yes	Yes	No	Shor ‘99 Regev’s reduction: CLZ22, YZ24, Jor+24 Planted inference: Has20, SOKB24
Compute a value	No	Yes	Yes	No	Condensed matter physics? Quantum chemistry?
Proof of quantumness	Yes, with key	Yes, with respect to key	No	Yes, under crypto assumptions	BCMVV21
Sampling	No	No	No	Almost, under complexity assumptions	BJS10, AA11, Google ‘20

We can categorize quantum algorithms by the form of their output. First, there are quantum algorithms for search problems, which produce a bitstring satisfying some constraints. This could be the prime factors of a number, a planted feature in some dataset, or the solution to an optimization problem. Next, there are quantum algorithms that compute a value to some precision, for example the expectation value of some physical observable. Then there are proofs of quantumness, which involve a verifier who generates a test using some hidden key, and the key can be used to verify the output. Finally, there are quantum algorithms which sample from some distribution.

Hamiltonian simulation is perhaps the most widely heralded source of quantum utility. Physics and chemistry contain many quantities that Nature computes effortlessly, yet remain beyond the reach of even our best classical simulations. Quantum computation is capable of simulating Nature directly, giving us strong reason to believe that quantum algorithms can compute classically-hard quantities.

There are already many examples where a quantum computer could help us answer an unsolved scientific question, like determining the phase diagram of the Hubbard model or the ground energy of FeMoCo. These undoubtedly have scientific value. However, they are isolated examples, whereas we would like evidence that the pool of quantum-solvable questions is inexhaustible. Can we take inspiration from strongly correlated physics to write down a concrete ensemble of Hamiltonian simulation instances where there is a classically-hard observable? This would gather evidence for the sustained, broad utility of quantum simulation, and would also help us understand where and how quantum advantage arises.

Over in the computer science community, there has been a lot of work on oracle separations such as welded trees and forrelation, which should give us confidence in the abilities of quantum computers. Can we instantiate these oracles in a way that pragmatically remains classically hard? This is necessary in order to pass our earlier litmus test of being ready to run the quantum algorithm tomorrow.

In addition to Hamiltonian simulation, there are several other broad classes of quantum algorithms, including quantum algorithms for linear systems of equations and differential equations, variational quantum algorithms for machine learning, and quantum algorithms for optimization. These frameworks sometimes come with proofs of BQP-completeness.

The issue with these broad frameworks is that they often do not specify a distribution over inputs. Can we find novel ensembles of inputs to these frameworks which exhibit super-quadratic speedups? BQP-completeness shows that one has translated the notion of quantum computation into a different language, which allows one to embed an existing quantum algorithm such as Shor’s algorithm into your framework. But in order to discover a new quantum algorithm, you must find an ensemble of BQP computations which does not arise from Shor’s algorithm.

Table I claims that sampling tasks alone are not useful since they are not even quantumly repeatable. One may wonder if sampling tasks could be useful in some way. After all, classical Monte Carlo sampling algorithms are widely used in practice. However, applications of sampling typically use samples to extract meaningful information or specific features of the underlying distribution. For example, Monte Carlo sampling can be used to evaluate integrals in Bayesian inference and statistical physics. In contrast, samples obtained from random quantum circuits lack any discernible features. If a collection of quantum algorithms generated samples containing meaningful signals from which one could extract classically hard-to-compute values, those algorithms would effectively transition into the compute a value category.

Table I also claims that proofs of quantumness are not useful. This is not completely true—one potential application is generating certifiable randomness. However, such applications are generally cryptographic rather than computational in nature. Specifically, proofs of quantumness cannot help us solve problems or answer questions whose solutions we do not already know.

Finally, there are several exciting directions proposing applications of quantum technologies in sensing and metrology, communication, learning with quantum memory, and streaming. These are very interesting, and I hope that mankind’s second century of quantum mechanics brings forth all flavors of capabilities. However, the technological momentum is mostly focused on building quantum computers for the purpose of computational advantage, and so this is where breakthroughs will have the greatest immediate impact.

Don’t be too afraid

At the annual QIP conference, only a handful of papers out of hundreds each year attempt to advance new quantum algorithms. Given the stakes, why is this number so low? One common explanation is that quantum algorithm research is simply too difficult. Nevertheless, we have seen substantial progress in quantum algorithms in recent years. After an underwhelming lack of end-to-end proposals with the potential for utility between the years 2000 and 2020, Table I exhibits several breakthroughs from the past 5 years.

In between blind optimism and resigned pessimism, embracing a mission-driven mindset can propel our field forward. We should allow ourselves to adopt a more exploratory, scrappier approach: We can hunt for quantum advantages in yet-unstudied problems or subtle signals in the third decimal place. The bar for meaningful progress is lower than it might seem, and even incremental advances are valuable. Don’t be too afraid!

Quadratic speedups are widespread but will not form the basis of practical quantum advantage due to the overheads associated with quantum error-correction. ↩︎

The first and second centuries of quantum mechanics

Posted on March 20, 2025 by preskill

At this week’s American Physical Society Global Physics Summit in Anaheim, California, John Preskill spoke at an event celebrating 100 years of groundbreaking advances in quantum mechanics. Here are his remarks.

Welcome, everyone, to this celebration of 100 years of quantum mechanics hosted by the Physical Review Journals. I’m John Preskill and I’m honored by this opportunity to speak today. I was asked by our hosts to express some thoughts appropriate to this occasion and to feel free to share my own personal journey as a physicist. I’ll embrace that charge, including the second part of it, perhaps even more that they intended. But over the next 20 minutes I hope to distill from my own experience some lessons of broader interest.

I began graduate study in 1975, the midpoint of the first 100 years of quantum mechanics, 50 years ago and 50 years after the discovery of quantum mechanics in 1925 that we celebrate here. So I’ll seize this chance to look back at where quantum physics stood 50 years ago, how far we’ve come since then, and what we can anticipate in the years ahead.

As an undergraduate at Princeton, I had many memorable teachers; I’ll mention just one: John Wheeler, who taught a full-year course for sophomores that purported to cover all of physics. Wheeler, having worked with Niels Bohr on nuclear fission, seemed implausibly old, though he was actually 61. It was an idiosyncratic course, particularly because Wheeler did not refrain from sharing with the class his current research obsessions. Black holes were a topic he shared with particular relish, including the controversy at the time concerning whether evidence for black holes had been seen by astronomers. Especially notably, when covering the second law of thermodynamics, he challenged us to ponder what would happen to entropy lost behind a black hole horizon, something that had been addressed by Wheeler’s graduate student Jacob Bekenstein, who had finished his PhD that very year. Bekenstein’s remarkable conclusion that black holes have an intrinsic entropy proportional to the event horizon area delighted the class, and I’ve had had many occasions to revisit that insight in the years since then. The lesson being that we should not underestimate the potential impact of sharing our research ideas with undergraduate students.

Stephen Hawking made that connection between entropy and area precise the very next year when he discovered that black holes radiate; his resulting formula for black hole entropy, a beautiful synthesis of relativity, quantum theory, and thermodynamics ranks as one of the shining achievements in the first 100 years of quantum mechanics. And it raised a deep puzzle pointed out by Hawking himself with which we have wrestled since then, still without complete success — what happens to information that disappears inside black holes?

Hawking’s puzzle ignited a titanic struggle between cherished principles. Quantum mechanics tells us that as quantum systems evolve, information encoded in a system can get scrambled into an unrecognizable form, but cannot be irreversibly destroyed. Relativistic causality tells us that information that falls into a black hole, which then evaporates, cannot possibly escape and therefore must be destroyed. Who wins – quantum theory or causality? A widely held view is that quantum mechanics is the victor, that causality should be discarded as a fundamental principle. This calls into question the whole notion of spacetime — is it fundamental, or an approximate property that emerges from a deeper description of how nature works? If emergent, how does it emerge and from what? Fully addressing that challenge we leave to the physicists of the next quantum century.

I made it to graduate school at Harvard and the second half century of quantum mechanics ensued. My generation came along just a little too late to take part in erecting the standard model of particle physics, but I was drawn to particle physics by that intoxicating experimental and theoretical success. And many new ideas were swirling around in the mid and late 70s of which I’ll mention only two. For one, appreciation was growing for the remarkable power of topology in quantum field theory and condensed matter, for example the theory of topological solitons. While theoretical physics and mathematics had diverged during the first 50 years of quantum mechanics, they have frequently crossed paths in the last 50 years, and topology continues to bring both insight and joy to physicists. The other compelling idea was to seek insight into fundamental physics at very short distances by searching for relics from the very early history of the universe. My first publication resulted from contemplating a question that connected topology and cosmology: Would magnetic monopoles be copiously produced in the early universe? To check whether my ideas held water, I consulted not a particle physicist or a cosmologist, but rather a condensed matter physicist (Bert Halperin) who provided helpful advice. The lesson being that scientific opportunities often emerge where different subfields intersect, a realization that has helped to guide my own research over the following decades.

Looking back at my 50 years as a working physicist, what discoveries can the quantumists point to with particular pride and delight?

I was an undergraduate when Phil Anderson proclaimed that More is Different, but as an arrogant would be particle theorist at the time I did not appreciate how different more can be. In the past 50 years of quantum mechanics no example of emergence was more stunning than the fractional quantum Hall effect. We all know full well that electrons are indivisible particles. So how can it be that in a strongly interacting two-dimensional gas an electron can split into quasiparticles each carrying a fraction of its charge? The lesson being: in a strongly-correlated quantum world, miracles can happen. What other extraordinary quantum phases of matter await discovery in the next quantum century?

Another thing I did not adequately appreciate in my student days was atomic physics. Imagine how shocked those who elucidated atomic structure in the 1920s would be by the atomic physics of today. To them, a quantum measurement was an action performed on a large ensemble of similarly prepared systems. Now we routinely grab ahold of a single atom, move it, excite it, read it out, and induce pairs of atoms to interact in precisely controlled ways. When interest in quantum computing took off in the mid-90s, it was ion-trap clock technology that enabled the first quantum processors. Strong coupling between single photons and single atoms in optical and microwave cavities led to circuit quantum electrodynamics, the basis for today’s superconducting quantum computers. The lesson being that advancing our tools often leads to new capabilities we hadn’t anticipated. Now clocks are so accurate that we can detect the gravitational redshift when an atom moves up or down by a millimeter in the earth’s gravitational field. Where will the clocks of the second quantum century take us?

Surely one of the great scientific triumphs of recent decades has been the success of LIGO, the laser interferometer gravitational-wave observatory. If you are a gravitational wave scientist now, your phone buzzes so often to announce another black hole merger that it’s become annoying. LIGO would not be possible without advanced laser technology, but aside from that what’s quantum about LIGO? When I came to Caltech in the early 1980s, I learned about a remarkable idea (from Carl Caves) that the sensitivity of an interferometer can be enhanced by a quantum strategy that did not seem at all obvious — injecting squeezed vacuum into the interferometer’s dark port. Now, over 40 years later, LIGO improves its detection rate by using that strategy. The lesson being that theoretical insights can enhance and transform our scientific and technological tools. But sometimes that takes a while.

What else has changed since 50 years ago? Let’s give thanks for the arXiv. When I was a student few scientists would type their own technical papers. It took skill, training, and patience to operate the IBM typewriters of the era. And to communicate our results, we had no email or world wide web. Preprints arrived by snail mail in Manila envelopes, if you were lucky enough to be on the mailing list. The Internet and the arXiv made scientific communication far faster, more convenient, and more democratic, and LaTeX made producing our papers far easier as well. And the success of the arXiv raises vexing questions about the role of journal publication as the next quantum century unfolds.

I made a mid-career shift in research direction, and I’m often asked how that came about. Part of the answer is that, for my generation of particle physicists, the great challenge and opportunity was to clarify the physics beyond the standard model, which we expected to provide a deeper understanding of how nature works. We had great hopes for the new phenomenology that would be unveiled by the Superconducting Super Collider, which was under construction in Texas during the early 90s. The cancellation of that project in 1993 was a great disappointment. The lesson being that sometimes our scientific ambitions are thwarted because the required resources are beyond what society will support. In which case, we need to seek other ways to move forward.

And then the next year, Peter Shor discovered the algorithm for efficiently finding the factors of a large composite integer using a quantum computer. Though computational complexity had not been part of my scientific education, I was awestruck by this discovery. It meant that the difference between hard and easy problems — those we can never hope to solve, and those we can solve with advanced technologies — hinges on our world being quantum mechanical. That excited me because one could anticipate that observing nature through a computational lens would deepen our understanding of fundamental science. I needed to work hard to come up to speed in a field that was new to me — teaching a course helped me a lot.

Ironically, for 4 ½ years in the mid-1980s I sat on the same corridor as Richard Feynman, who had proposed the idea of simulating nature with quantum computers in 1981. And I never talked to Feynman about quantum computing because I had little interest in that topic at the time. But Feynman and I did talk about computation, and in particular we were both very interested in what one could learn about quantum chromodynamics from Euclidean Monte Carlo simulations on conventional computers, which were starting to ramp up in that era. Feynman correctly predicted that it would be a few decades before sufficient computational power would be available to make accurate quantitative predictions about nonperturbative QCD. But it did eventually happen — now lattice QCD is making crucial contributions to the particle physics and nuclear physics programs. The lesson being that as we contemplate quantum computers advancing our understanding of fundamental science, we should keep in mind a time scale of decades.

Where might the next quantum century take us? What will the quantum computers of the future look like, or the classical computers for that matter? Surely the qubits of 100 years from now will be much different and much better than what we have today, and the machine architecture will no doubt be radically different than what we can currently envision. And how will we be using those quantum computers? Will our quantum technology have transformed medicine and neuroscience and our understanding of living matter? Will we be building materials with astonishing properties by assembling matter atom by atom? Will our clocks be accurate enough to detect the stochastic gravitational wave background and so have reached the limit of accuracy beyond which no stable time standard can even be defined? Will quantum networks of telescopes be observing the universe with exquisite precision and what will that reveal? Will we be exploring the high energy frontier with advanced accelerators like muon colliders and what will they teach us? Will we have identified the dark matter and explained the dark energy? Will we have unambiguous evidence of the universe’s inflationary origin? Will we have computed the parameters of the standard model from first principles, or will we have convinced ourselves that’s a hopeless task? Will we have understood the fundamental constituents from which spacetime itself is composed?

There is an elephant in the room. Artificial intelligence is transforming how we do science at a blistering pace. What role will humans play in the advancement of science 100 years from now? Will artificial intelligence have melded with quantum intelligence? Will our instruments gather quantum data Nature provides, transduce it to quantum memories, and process it with quantum computers to discern features of the world that would otherwise have remained deeply hidden?

To a limited degree, in contemplating the future we are guided by the past. Were I asked to list the great ideas about physics to surface over the 50-year span of my career, there are three in particular I would nominate for inclusion on that list. (1) The holographic principle, our best clue about how gravity and quantum physics fit together. (2) Topological quantum order, providing ways to distinguish different phases of quantum matter when particles strongly interact with one another. (3) And quantum error correction, our basis for believing we can precisely control very complex quantum systems, including advanced quantum computers. It’s fascinating that these three ideas are actually quite closely related. The common thread connecting them is that all relate to the behavior of many-particle systems that are highly entangled.

Quantum error correction is the idea that we can protect quantum information from local noise by encoding the information in highly entangled states such that the protected information is inaccessible locally, when we look at just a few particles at a time. Topological quantum order is the idea that different quantum phases of matter can look the same when we observe them locally, but are distinguished by global properties hidden from local probes — in other words such states of matter are quantum memories protected by quantum error correction. The holographic principle is the idea that all the information in a gravitating three-dimensional region of space can be encoded by mapping it to a local quantum field theory on the two-dimensional boundary of the space. And that map is in fact the encoding map of a quantum error-correcting code. These ideas illustrate how as our knowledge advances, different fields of physics are converging on common principles. Will that convergence continue in the second century of quantum mechanics? We’ll see.

As we contemplate the long-term trajectory of quantum science and technology, we are hampered by our limited imaginations. But one way to loosely characterize the difference between the past and the future of quantum science is this: For the first hundred years of quantum mechanics, we achieved great success at understanding the behavior of weakly correlated many-particles systems relevant to for example electronic structure, atomic and molecular physics, and quantum optics. The insights gained regarding for instance how electrons are transported through semiconductors or how condensates of photons and atoms behave had invaluable scientific and technological impact. The grand challenge and opportunity we face in the second quantum century is acquiring comparable insight into the complex behavior of highly entangled states of many particles which are well beyond the reach of current theory or computation. This entanglement frontier is vast, inviting, and still largely unexplored. The wonders we encounter in the second century of quantum mechanics, and their implications for human civilization, are bound to supersede by far those of the first century. So let us gratefully acknowledge the quantum heroes of the past and present, and wish good fortune to the quantum explorers of the future.

Lessons in frustration

Posted on February 16, 2025 by Nicole Yunger Halpern

Assa Auerbach’s course was the most maddening course I’ve ever taken.

I was a master’s student in the Perimeter Scholars International program at the Perimeter Institute for Theoretical Physics. Perimeter trotted in world experts to lecture about modern physics. Many of the lecturers dazzled us with their pedagogy and research. We grew to know them not only in class and office hours, but also over meals at Perimeter’s Black-Hole Bistro.

Assa hailed from the Technion in Haifa, Israel. He’d written the book—at least, a book—about condensed matter, the physics of materials. He taught us condensed matter, according to some definition of “taught.”

Assa zipped through course material. He refrained from defining terminology. He used loose, imprecise language that conveys intuition to experts and only to experts. He threw at us the Hubbard model, the Heisenberg model, the Meissner effect, and magnons. If you don’t know what those terms mean, then I empathize. Really.

So I fought Assa like a groom hauling on a horse’s reins. I raised my hand again and again, insisting on clarifications. I shot off questions as quickly as I could invent them, because they were the only barriers slowing him down. He told me they were.

One day, we were studying magnetism. It arises because each atom in a magnet has a magnetic moment, a tiny compass that can angle in any direction. Under certain conditions, atoms’ magnetic moments tend to angle in opposite directions. Sometimes, not all atoms can indulge this tendency, as in the example below.

Physicists call this clash frustration, which I wanted to understand comprehensively and abstractly. But Assa wouldn’t define frustration; he’d only sketch an example.

But what is frustration? I insisted.

It’s when the atoms aren’t happy, he said, like you are now.

After class, I’d escape to the bathroom and focus on breathing. My body felt as though it had been battling an assailant physically.

Earlier this month, I learned that Assa had passed away suddenly. A former Perimeter classmate reposted the Technion’s news blurb on Facebook. A photo of Assa showed a familiar smile flashing beneath curly salt-and-pepper hair.

Am I defaming the deceased? No. The news of Assa’s passing walloped me as hard as any lecture of his did. I liked Assa and respected him; he was a researcher’s researcher. And I liked Assa for liking me for fighting to learn.

One day, at the Bistro, Assa explained why the class had leaped away from the foundations of condensed matter into advanced topics so quickly: earlier discoveries felt “stale” to him. Everyone, he believed, could smell their moldiness. I disagreed, although I didn’t say so: decades-old discoveries qualify as new to anyone learning about them for the first time. Besides, 17th-century mechanics and 19th-century thermodynamics soothe my soul. But I respected Assa’s enthusiasm for the cutting-edge. And I did chat with him at the Bistro, where his friendliness shone like that smile.

Five years later, I was sojourning at the Kavli Institute for Theoretical Physics (KITP) in Santa Barbara, near the end of my PhD. The KITP, like Perimeter, draws theorists from across the globe. I spotted Assa among them and reached out about catching up. We discussed thermodynamics and experiments and travel.

Assa confessed that, at Perimeter, he’d been lecturing to himself—presenting lectures that he’d have enjoyed hearing, rather than lectures designed for master’s students. He’d appreciated my slowing him down. Once, he explained, he’d guest-lectured at Harvard. Nobody asked questions, so he assumed that the students must have known the material already, that he must have been boring them. So he sped up. Nobody said anything, so he sped up further. At the end, he discovered that nobody had understood any of his material. So he liked having an objector keeping him in check.

And where had this objector ended up? In a PhD program and at a mecca for theoretical physicists. Pursuing the cutting edge, a budding researcher’s researcher. I’d angled in the same direction as my former teacher. And one Perimeter classmate, a faculty member specializing in condensed matter today, waxed even more eloquently about Assa’s inspiration when we were students.

Physics needs more scientists like Assa: nose to the wind, energetic, low on arrogance. Someone who’d respond to this story of frustration with that broad smile.

Ten lessons I learned from John Preskill

Posted on January 19, 2025 by Nicole Yunger Halpern

Last August, Toronto’s Centre for Quantum Information and Quantum Control (CQIQC) gave me 35 minutes to make fun of John Preskill in public. CQIQC was hosting its biannual conference, also called CQIQC, in Toronto. The conference features the awarding of the John Stewart Bell Prize for fundamental quantum physics. The prize derives its name for the thinker who transformed our understanding of entanglement. John received this year’s Bell Prize for identifying, with collaborators, how we can learn about quantum states from surprisingly few trials and measurements.

The organizers invited three Preskillites to present talks in John’s honor: Hoi-Kwong Lo, who’s helped steer quantum cryptography and communications; Daniel Gottesman, who’s helped lay the foundations of quantum error correction; and me. I believe that one of the most fitting ways to honor John is by sharing the most exciting physics you know of. I shared about quantum thermodynamics for (simple models of) nuclear physics, along with ten lessons I learned from John. You can watch the talk here and check out the paper, recently published in Physical Review Letters, for technicalities.

John has illustrated this lesson by wrestling with the black-hole-information paradox, including alongside Stephen Hawking. Quantum information theory has informed quantum thermodynamics, as Quantum Frontiers regulars know. Quantum thermodynamics is the study of work (coordinated energy that we can harness directly) and heat (the energy of random motion). Systems exchange heat with heat reservoirs—large, fixed-temperature systems. As I draft this blog post, for instance, I’m radiating heat into the frigid air in Montreal Trudeau Airport.

So much for quantum information. How about high-energy physics? I’ll include nuclear physics in the category, as many of my Europeans colleagues do. Much of nuclear physics and condensed matter involves gauge theories. A gauge theory is a model that contains more degrees of freedom than the physics it describes. Similarly, a friend’s description of the CN Tower could last twice as long as necessary, due to redundancies. Electrodynamics—the theory behind light bulbs—is a gauge theory. So is quantum chromodynamics, the theory of the strong force that holds together a nucleus’s constituents.

Every gauge theory obeys Gauss’s law. Gauss’s law interrelates the matter at a site to the gauge field around the site. For example, imagine a positive electric charge in empty space. An electric field—a gauge field—points away from the charge at every spot in space. Imagine a sphere that encloses the charge. How much of the electric field is exiting the sphere? The answer depends on the amount of charge inside, according to Gauss’s law.

Gauss’s law interrelates the matter at a site with the gauge field nearby…which is related to the matter at the next site…which is related to the gauge field farther away. So everything depends on everything else. So we can’t easily claim that over here are independent degrees of freedom that form a system of interest, while over there are independent degrees of freedom that form a heat reservoir. So how can we define the heat and work exchanged within a lattice gauge theory? If we can’t, we should start biting our nails: thermodynamics is the queen of the physical theories, a metatheory expected to govern all other theories. But how can we define the quantum thermodynamics of lattice gauge theories? My colleague Zohreh Davoudi and her group asked me this question.

I had the pleasure of addressing the question with five present and recent Marylanders…

…the mention of whom in my CQIQC talk invited…

I’m a millennial; social media took off with my generation. But I enjoy saying that my PhD advisor enjoys far more popularity on social media than I do.

How did we begin establishing a quantum thermodynamics for lattice gauge theories?

Someone who had a better idea than I, when I embarked upon this project, was my colleague Chris Jarzynski. So did Dvira Segal, a University of Toronto chemist and CQIQC’s director. So did everyone else who’d helped develop the toolkit of strong-coupling thermodynamics. I’d only heard of the toolkit, but I thought it sounded useful for lattice gauge theories, so I invited Chris to my conversations with Zohreh’s group.

I didn’t create this image for my talk, believe it or not. The picture already existed on the Internet, courtesy of this blog.

Strong-coupling thermodynamics concerns systems that interact strongly with reservoirs. System–reservoir interactions are weak, or encode little energy, throughout much of thermodynamics. For example, I exchange little energy with Montreal Trudeau’s air, relative to the amount of energy inside me. The reason is, I exchange energy only through my skin. My skin forms a small fraction of me because it forms my surface. My surface is much smaller than my volume, which is proportional to the energy inside me. So I couple to Montreal Trudeau’s air weakly.

My surface would be comparable to my volume if I were extremely small—say, a quantum particle. My interaction with the air would encode loads of energy—an amount comparable to the amount inside me. Should we count that interaction energy as part of my energy or as part of the air’s energy? Could we even say that I existed, and had a well-defined form, independently of that interaction energy? Strong-coupling thermodynamics provides a framework for answering these questions.

Kevin Kuns, a former *Quantum Frontiers* blogger, described how John explains physics through simple concepts, like a ball attached to a spring. John’s gentle, soothing voice resembles a snake charmer’s, Kevin wrote. John charms his listeners into returning to their textbooks and brushing up on basic physics.

Little is more basic than the first law of thermodynamics, synopsized as energy conservation. The first law governs how much a system’s internal energy changes during any process. The energy change equals the heat absorbed, plus the work absorbed, by the system. Every formulation of thermodynamics should obey the first law—including strong-coupling thermodynamics.

Which lattice-gauge-theory processes should we study, armed with the toolkit of strong-coupling thermodynamics? My collaborators and I implicitly followed

and

We don’t want to irritate experimentalists by asking them to run difficult protocols. Tom Rosenbaum, on the left of the previous photograph, is a quantum experimentalist. He’s also the president of Caltech, so John has multiple reasons to want not to irritate him.

Quantum experimentalists have run quench protocols on many quantum simulators, or special-purpose quantum computers. During a quench protocol, one changes a feature of the system quickly. For example, many quantum systems consist of particles hopping across a landscape of hills and valleys. One might flatten a hill during a quench.

We focused on a three-step quench protocol: (1) Set the system up in its initial landscape. (2) Quickly change the landscape within a small region. (3) Let the system evolve under its natural dynamics for a long time. Step 2 should cost work. How can we define the amount of work performed? By following

John wrote a blog post about how the typical physicist is a one-trick pony: they know one narrow subject deeply. John prefers to know two subjects. He can apply insights from one field to the other. A two-trick pony can show that Gauss’s law behaves like a strong interaction—that lattice gauge theories are strongly coupled thermodynamic systems. Using strong-coupling thermodynamics, the two-trick pony can define the work (and heat) exchanged within a lattice gauge theory.

An experimentalist can easily measure the amount of work performed,¹ we expect, for two reasons. First, the experimentalist need measure only the small region where the landscape changed. Measuring the whole system would be tricky, because it’s so large and it can contain many particles. But an experimentalist can control the small region. Second, we proved an equation that should facilitate experimental measurements. The equation interrelates the work performed¹ with a quantity that seems experimentally accessible.

My team applied our work definition to a lattice gauge theory in one spatial dimension—a theory restricted to living on a line, like a caterpillar on a thin rope. You can think of the matter as qubits² and the gauge field as more qubits. The system looks identical if you flip it upside-down; that is, the theory has a $\mathbb{Z}_2$ symmetry. The system has two phases, analogous to the liquid and ice phases of H $_2$ O. Which phase the system occupies depends on the chemical potential—the average amount of energy needed to add a particle to the system (while the system’s entropy, its volume, and more remain constant).

My coauthor Connor simulated the system numerically, calculating its behavior on a classical computer. During the simulated quench process, the system began in one phase (like H $_2$ O beginning as water). The quench steered the system around within the phase (as though changing the water’s temperature) or across the phase transition (as though freezing the water). Connor computed the work performed during the quench.¹ The amount of work changed dramatically when the quench started steering the system across the phase transition.

Not only could we define the work exchanged within a lattice gauge theory, using strong-coupling quantum thermodynamics. Also, that work signaled a phase transition—a large-scale, qualitative behavior.

What future do my collaborators and I dream of for our work? First, we want for an experimentalist to measure the work¹ spent on a lattice-gauge-theory system in a quantum simulation. Second, we should expand our definitions of quantum work and heat beyond sudden-quench processes. How much work and heat do particles exchange while scattering in particle accelerators, for instance? Third, we hope to identify other phase transitions and macroscopic phenomena using our work and heat definitions. Fourth—most broadly—we want to establish a quantum thermodynamics for lattice gauge theories.

Five years ago, I didn’t expect to be collaborating on lattice gauge theories inspired by nuclear physics. But this work is some of the most exciting I can think of to do. I hope you think it exciting, too. And, more importantly, I hope John thought it exciting in Toronto.

I was a student at Caltech during “One Entangled Evening,” the campus-wide celebration of Richard Feynman’s 100th birthday. So I watched John sing and dance onstage, exhibiting no fear of embarrassing himself. That observation seemed like an appropriate note on which to finish with my slides…and invite questions from the audience.

Congratulations on your Bell Prize, John.

¹Really, the dissipated work.

²Really, hardcore bosons.

Finding Ed Jaynes’s ghost

Posted on December 22, 2024 by Nicole Yunger Halpern

You might have heard of the conundrum “What do you give the man who has everything?” I discovered a variation on it last October: how do you celebrate the man who studied (nearly) everything? Physicist Edwin Thompson Jaynes impacted disciplines from quantum information theory to biomedical imaging. I almost wrote “theoretical physicist,” instead of “physicist,” but a colleague insisted that Jaynes had a knack for electronics and helped design experiments, too. Jaynes worked at Washington University in St. Louis (WashU) from 1960 to 1992. I’d last visited the university in 2018, as a newly minted postdoc collaborating with WashU experimentalist Kater Murch. I’d scoured the campus for traces of Jaynes like a pilgrim seeking a saint’s forelock or humerus. The blog post “Chasing Ed Jaynes’s ghost” documents that hunt.

I found his ghost this October.

Kater and colleagues hosted the Jaynes Centennial Symposium on a brilliant autumn day when the campus’s trees were still contemplating shedding their leaves. The agenda featured researchers from across the sciences and engineering. We described how Jaynes’s legacy has informed 21st-century developments in quantum information theory, thermodynamics, biophysics, sensing, and computation. I spoke about quantum thermodynamics and information theory—specifically, incompatible conserved quantities, about which my research-group members and I have blogged many times.

Irfan Siddiqi spoke about quantum technologies. An experimentalist at the University of California, Berkeley, Irfan featured on Quantum Frontiers seven years ago. His lab specializes in superconducting qubits, tiny circuits in which current can flow forever, without dissipating. How can we measure a superconducting qubit? We stick the qubit in a box. Light bounces back and forth across the box. The light interacts with the qubit while traversing it, in accordance with the Jaynes–Cummings model. We can’t seal any box perfectly, so some light will leak out. That light carries off information about the qubit. We can capture the light using a photodetector to infer about the qubit’s state.

Bill Bialek, too, spoke about inference. But Bill is a Princeton biophysicist, so fruit flies preoccupy him more than qubits do. A fruit fly metamorphoses from a maggot that hatches from an egg. As the maggot develops, its cells differentiate: some form a head, some form a tail, and so on. Yet all the cells contain the same genetic information. How can a head ever emerge, to differ from a tail?

A fruit-fly mother, Bill revealed, injects molecules into an egg at certain locations. These molecules diffuse across the egg, triggering the synthesis of more molecules. The knock-on molecules’ concentrations can vary strongly across the egg: a maggot’s head cells contain molecules at certain concentrations, and the tail cells contain the same molecules at other concentrations.

At this point in Bill’s story, I was ready to take my hat off to biophysicists for answering the question above, which I’ll rephrase here: if we find that a certain cell belongs to a maggot’s tail, why does the cell belong to the tail? But I enjoyed even more how Bill turned the question on its head (pun perhaps intended): imagine that you’re a maggot cell. How can you tell where in the maggot you are, to ascertain how to differentiate? Nature asks this question (loosely speaking), whereas human observers ask Bill’s first question.

To answer the second question, Bill recalled which information a cell accesses. Suppose you know four molecules’ concentrations: $c_1$ , $c_2$ , $c_3$ , and $c_4$ . How accurately can you predict the cell’s location? That is, what probability does the cell have of sitting at some particular site, conditioned on the $c$ s? That probability is large only at one site, biophysicists have found empirically. So a cell can accurately infer its position from its molecules’ concentrations.

I’m no biophysicist (despite minor evidence to the contrary), but I enjoyed Bill’s story as I enjoyed Irfan’s. Probabilities, information, and inference are abstract notions; yet they impact physical reality, from insects to quantum science. This tension between abstraction and concreteness arrested me when I first encountered entropy, in a ninth-grade biology lecture. The tension drew me into information theory and thermodynamics. These toolkits permeate biophysics as they permeate my disciplines. So, throughout the symposium, I spoke with engineers, medical-school researchers, biophysicists, thermodynamicists, and quantum scientists. They all struck me as my kind of people, despite our distribution across the intellectual landscape. Jaynes reasoned about distributions—probability distributions—and I expect he’d have approved of this one. The man who studied nearly everything deserves a celebration that illuminates nearly everything.

Happy 200th birthday, Carnot’s theorem!

Posted on November 28, 2024 by Nicole Yunger Halpern

In Kenneth Grahame’s 1908 novel The Wind in the Willows, a Mole meets a Water Rat who lives on a River. The Rat explains how the River permeates his life: “It’s brother and sister to me, and aunts, and company, and food and drink, and (naturally) washing.” As the River plays many roles in the Rat’s life, so does Carnot’s theorem play many roles in a thermodynamicist’s.

Nicolas Léonard Sadi Carnot lived in France during the turn of the 19th century. His father named him Sadi after the 13th-century Persian poet Saadi Shirazi. Said father led a colorful life himself,¹ working as a mathematician, engineer, and military commander for and before the Napoleonic Empire. Sadi Carnot studied in Paris at the École Polytechnique, whose members populate a “Who’s Who” list of science and engineering.

As Carnot grew up, the Industrial Revolution was humming. Steam engines were producing reliable energy on vast scales; factories were booming; and economies were transforming. France’s old enemy Britain enjoyed two advantages. One consisted of inventors: Englishmen Thomas Savery and Thomas Newcomen invented the steam engine. Scotsman James Watt then improved upon Newcomen’s design until rendering it practical. Second, northern Britain contained loads of coal that industrialists could mine to power her engines. France had less coal. So if you were a French engineer during Carnot’s lifetime, you should have cared about engines’ efficiencies—how effectively engines used fuel.²

Carnot proved a fundamental limitation on engines’ efficiencies. His theorem governs engines that draw energy from heat—rather than from, say, the motional energy of water cascading down a waterfall. In Carnot’s argument, a heat engine interacts with a cold environment and a hot environment. (Many car engines fall into this category: the hot environment is burning gasoline. The cold environment is the surrounding air into which the car dumps exhaust.) Heat flows from the hot environment to the cold. The engine siphons off some heat and converts it into work. Work is coordinated, well-organized energy that one can directly harness to perform a useful task, such as turning a turbine. In contrast, heat is the disordered energy of particles shuffling about randomly. Heat engines transform random heat into coordinated work.

In *The Wind and the Willows*, Toad drives motorcars likely powered by internal combustion, rather than by a steam engine of the sort that powered the Industrial Revolution.

An engine’s efficiency is the bang we get for our buck—the upshot we gain, compared to the cost we spend. Running an engine costs the heat that flows between the environments: the more heat flows, the more the hot environment cools, so the less effectively it can serve as a hot environment in the future. An analogous statement concerns the cold environment. So a heat engine’s efficiency is the work produced, divided by the heat spent.

Carnot upper-bounded the efficiency achievable by every heat engine of the sort described above. Let $T_{\rm C}$ denote the cold environment’s temperature; and $T_{\rm H}$ , the hot environment’s. The efficiency can’t exceed $1 - \frac{ T_{\rm C} }{ T_{\rm H} }$ . What a simple formula for such an extensive class of objects! Carnot’s theorem governs not only many car engines (Otto engines), but also the Stirling engine that competed with the steam engine, its cousin the Ericsson engine, and more.

In addition to generality and simplicity, Carnot’s bound boasts practical and fundamental significances. Capping engine efficiencies caps the output one can expect of a machine, factory, or economy. The cap also prevents engineers from wasting their time on daydreaming about more-efficient engines.

More fundamentally than these applications, Carnot’s theorem encapsulates the second law of thermodynamics. The second law helps us understand why time flows in only one direction. And what’s deeper or more foundational than time’s arrow? People often cast the second law in terms of entropy, but many equivalent formulations express the law’s contents. The formulations share a flavor often synopsized with “You can’t win.” Just as we can’t grow younger, we can’t beat Carnot’s bound on engines.

Video courtesy of FQxI

One might expect no engine to achieve the greatest efficiency imaginable: $1 - \frac{ T_{\rm C} }{ T_{\rm H} }$ , called the Carnot efficiency. This expectation is incorrect in one way and correct in another. Carnot did design an engine that could operate at his eponymous efficiency: an eponymous engine. A Carnot engine can manifest as the thermodynamicist’s favorite physical system: a gas in a box topped by a movable piston. The gas undergoes four strokes, or steps, to perform work. The strokes form a closed cycle, returning the gas to its initial conditions.³

Steampunk artist Todd Cahill beautifully illustrated the Carnot cycle for my book. The gas performs useful work because a weight sits atop the piston. Pushing the piston upward, the gas lifts the weight.

The gas expands during stroke 1, pushing the piston and so outputting work. Maintaining contact with the hot environment, the gas remains at the temperature $T_{\rm H}$ . The gas then disconnects from the hot environment. Yet the gas continues to expand throughout stroke 2, lifting the weight further. Forfeiting energy, the gas cools. It ends stroke 2 at the temperature $T_{\rm C}$ .

The gas contacts the cold environment throughout stroke 3. The piston pushes on the gas, compressing it. At the end of the stroke, the gas disconnects from the cold environment. The piston continues compressing the gas throughout stroke 4, performing more work on the gas. This work warms the gas back up to $T_{\rm H}$ .

In summary, Carnot’s engine begins hot, performs work, cools down, has work performed on it, and warms back up. The gas performs more work on the piston than the piston performs on it.

At what cost, if the engine operates at the Carnot efficiency? The engine mustn’t waste heat. One wastes heat by roiling up the gas unnecessarily—by expanding or compressing it too quickly. The gas must stay in equilibrium, a calm, quiescent state. One can keep the gas quiescent only by running the cycle infinitely slowly. The cycle will take an infinitely long time, outputting zero power (work per unit time). So one can achieve the perfect efficiency only in principle, not in practice, and only by sacrificing power. Again, you can’t win.

Carnot’s theorem may sound like the Eeyore of physics, all negativity and depression. But I view it as a companion and backdrop as rich, for thermodynamicists, as the River is for the Water Rat. Carnot’s theorem curbs diverse technologies in practical settings. It captures the second law, a foundational principle. The Carnot cycle provides intuition, serving as a simple example on which thermodynamicists try out new ideas, such as quantum engines. Carnot’s theorem also provides what physicists call a sanity check: whenever a researcher devises a new (for example, quantum) heat engine, they can confirm that the engine obeys Carnot’s theorem, to help confirm their proposal’s accuracy. Carnot’s theorem also serves as a school exercise and a historical tipping point: the theorem initiated the development of thermodynamics, which continues to this day.

So Carnot’s theorem is practical and fundamental, pedagogical and cutting-edge—brother and sister, and aunts, and company, and food and drink. I just wouldn’t recommend trying to wash your socks in Carnot’s theorem.

¹To a theoretical physicist, working as a mathematician and an engineer amounts to leading a colorful life.

²People other than Industrial Revolution–era French engineers should care, too.

³A cycle doesn’t return the hot and cold environments to their initial conditions, as explained above.

Now published: Building Quantum Computers

Posted on September 28, 2024 by preskill

Building Quantum Computers: A Practical Introduction by Shayan Majidy, Christopher Wilson, and Raymond Laflamme has been published by Cambridge University Press and will be released in the US on September 30. The authors invited me to write a Foreword for the book, which I was happy to do. The publisher kindly granted permission for me to post the Foreword here on Quantum Frontiers.

Foreword

The principles of quantum mechanics, which as far as we know govern all natural phenomena, were discovered in 1925. For 99 years we have built on that achievement to reach a comprehensive understanding of much of the physical world, from molecules to materials to elementary particles and much more. No comparably revolutionary advance in fundamental science has occurred since 1925. But a new revolution is in the offing.

Up until now, most of what we have learned about the quantum world has resulted from considering the behavior of individual particles — for example a single electron propagating as a wave through a crystal, unfazed by barriers that seem to stand in its way. Understanding that single-particle physics has enabled us to explore nature in unprecedented ways, and to build information technologies that have profoundly transformed our lives.

What’s happening now is we’re learning how to instruct particles to evolve in coordinated ways that can’t be accurately described in terms of the behavior of one particle at a time. The particles, as we like to say, can become entangled. Many particles, like electrons or photons or atoms, when highly entangled, exhibit an extraordinary complexity that we can’t capture with the most powerful of today’s supercomputers, or with our current theories of how nature works. That opens extraordinary opportunities for new discoveries and new applications.

Most temptingly, we anticipate that by building and operating large-scale quantum computers, which control the evolution of very complex entangled quantum systems, we will be able to solve some computational problems that are far beyond the reach of today’s digital computers. The concept of a quantum computer was proposed over 40 years ago, and the task of building quantum computing hardware has been pursued in earnest since the 1990s. After decades of steady progress, quantum information processors with hundreds of qubits have become feasible and are scientifically valuable. But we may need quantum processors with millions of qubits to realize practical applications of broad interest. There is still a long way to go.

Why is it taking so long? A conventional computer processes bits, where each bit could be, say, a switch which is either on or off. To build highly complex entangled quantum states, the fundamental information-carrying component of a quantum computer must be what we call a “qubit” rather than a bit. The trouble is that qubits are much more fragile than bits — when a qubit interacts with its environment, the information it carries is irreversibly damaged, a process called decoherence. To perform reliable logical operations on qubits, we need to prevent decoherence by keeping the qubits nearly perfectly isolated from their environment. That’s very hard to do. And because a qubit, unlike a bit, can change continuously, precisely controlling a qubit is a further challenge, even when decoherence is in check.

While theorists may find it convenient to regard a qubit (or a bit) as an abstract object, in an actual processor a qubit needs to be encoded in a particular physical system. There are many options. It might, for example, be encoded in a single atom which can be in either one of two long-lived internal states. Or the spin of a single atomic nucleus or electron which points either up or down along some axis. Or a single photon that occupies either one of two possible optical modes. These are all remarkable encodings, because the qubit resides in a very simple single quantum system, yet, thanks to technical advances over several decades, we have learned to control such qubits reasonably well. Alternatively, the qubit could be encoded in a more complex system, like a circuit conducting electricity without resistance at very low temperature. This is also remarkable, because although the qubit involves the collective motion of billions of pairs of electrons, we have learned to make it behave as though it were a single atom.

To run a quantum computer, we need to manipulate individual qubits and perform entangling operations on pairs of qubits. Once we can perform such single-qubit and two-qubit “quantum gates” with sufficient accuracy, and measure and initialize the qubits as well, then in principle we can perform any conceivable quantum computation by assembling sufficiently many qubits and executing sufficiently many gates.

It’s a daunting engineering challenge to build and operate a quantum system of sufficient complexity to solve very hard computation problems. That systems engineering task, and the potential practical applications of such a machine, are both beyond the scope of Building Quantum Computers. Instead the focus is on the computer’s elementary constituents for four different qubit modalities: nuclear spins, photons, trapped atomic ions, and superconducting circuits. Each type of qubit has its own fascinating story, told here expertly and with admirable clarity.

For each modality a crucial question must be addressed: how to produce well-controlled entangling interactions between two qubits. Answers vary. Spins have interactions that are always on, and can be “refocused” by applying suitable pulses. Photons hardly interact with one another at all, but such interactions can be mocked up using appropriate measurements. Because of their Coulomb repulsion, trapped ions have shared normal modes of vibration that can be manipulated to generate entanglement. Couplings and frequencies of superconducting qubits can be tuned to turn interactions on and off. The physics underlying each scheme is instructive, with valuable lessons for the quantum informationists to heed.

Various proposed quantum information processing platforms have characteristic strengths and weaknesses, which are clearly delineated in this book. For now it is important to pursue a variety of hardware approaches in parallel, because we don’t know for sure which ones have the best long term prospects. Furthermore, different qubit technologies might be best suited for different applications, or a hybrid of different technologies might be the best choice in some settings. The truth is that we are still in the early stages of developing quantum computing systems, and there is plenty of potential for surprises that could dramatically alter the outlook.

Building large-scale quantum computers is a grand challenge facing 21st-century science and technology. And we’re just getting started. The qubits and quantum gates of the distant future may look very different from what is described in this book, but the authors have made wise choices in selecting material that is likely to have enduring value. Beyond that, the book is highly accessible and fun to read. As quantum technology grows ever more sophisticated, I expect the study and control of highly complex many-particle systems to become an increasingly central theme of physical science. If so, Building Quantum Computers will be treasured reading for years to come.

John Preskill
Pasadena, California

Announcing the quantum-steampunk creative-writing course!

Posted on September 18, 2024 by Nicole Yunger Halpern

Why not run a quantum-steampunk creative-writing course?

Quantum steampunk, as Quantum Frontiers regulars know, is the aesthetic and spirit of a growing scientific field. Steampunk is a subgenre of science fiction. In it, futuristic technologies invade Victorian-era settings: submarines, time machines, and clockwork octopodes populate La Belle Èpoque, a recently liberated Haiti, and Sherlock Holmes’s London. A similar invasion characterizes my research field, quantum thermodynamics: thermodynamics is the study of heat, work, temperature, and efficiency. The Industrial Revolution spurred the theory’s development during the 1800s. The theory’s original subject—nineteenth-century engines—were large, were massive, and contained enormous numbers of particles. Such engines obey the classical mechanics developed during the 1600s. Hence thermodynamics needs re-envisioning for quantum systems. To extend the theory’s laws and applications, quantum thermodynamicists use mathematical and experimental tools from quantum information science. Quantum information science is, in part, the understanding of quantum systems through how they store and process information. The toolkit is partially cutting-edge and partially futuristic, as full-scale quantum computers remain under construction. So applying quantum information to thermodynamics—quantum thermodynamics—strikes me as the real-world incarnation of steampunk.

But the thought of a quantum-steampunk creative-writing course had never occurred to me, and I hesitated over it. Quantum-steampunk blog posts, I could handle. A book, I could handle. Even a short-story contest, I’d handled. But a course? The idea yawned like the pitch-dark mouth of an unknown cavern in my imagination.

But the more I mulled over Edward Daschle’s suggestion, the more I warmed to it. Edward was completing a master’s degree in creative writing at the University of Maryland (UMD), specializing in science fiction. His mentor Emily Brandchaft Mitchell had sung his praises via email. In 2023, Emily had served as a judge for the Quantum-Steampunk Short-Story Contest. She works as a professor of English at UMD, writes fiction, and specializes in the study of genre. I reached out to her last spring about collaborating on a grant for quantum-inspired art, and she pointed to her protégé.

Who won me over. Edward and I are co-teaching “Writing Quantum Steampunk: Science-Fiction Workshop” during spring 2025.

The course will alternate between science and science fiction. Under Edward’s direction, we’ll read and discuss published fiction. We’ll also learn about what genres are and how they come to be. Students will try out writing styles by composing short stories themselves. Everyone will provide feedback about each other’s writing: what works, what’s confusing, and opportunities for improvement.

The published fiction chosen will mirror the scientific subjects we’ll cover: quantum physics; quantum technologies; and thermodynamics, including quantum thermodynamics. I’ll lead this part of the course. The scientific studies will interleave with the story reading, writing, and workshopping. Students will learn about the science behind the science fiction while contributing to the growing subgenre of quantum steampunk.

We aim to attract students from across campus: physics, English, the Jiménez-Porter Writers’ House, computer science, mathematics, and engineering—plus any other departments whose students have curiosity and creativity to spare. The course already has four cross-listings—Arts and Humanities 270, Physics 299Q, Computer Science 298Q, and Mechanical Engineering 299Q—and will probably acquire a fifth (Chemistry 298Q). You can earn a Distributive Studies: Scholarship in Practice (DSSP) General Education requirement, and undergraduate and graduate students are welcome. QuICS—the Joint Center for Quantum Information and Computer Science, my home base—is paying Edward’s salary through a seed grant. Ross Angelella, the director of the Writers’ House, arranged logistics and doused us with enthusiasm. I’m proud of how organizations across the university are uniting to support the course.

The diversity we seek, though, poses a challenge. The course lacks prerequisites, so I’ll need to teach at a level comprehensible to the non-science students. I’d enjoy doing so, but I’m concerned about boring the science students. Ideally, the science students will help me teach, while the non-science students will challenge us with foundational questions that force us to rethink basic concepts. Also, I hope that non-science students will galvanize discussions about ethical and sociological implications of quantum technologies. But how can one ensure that conversation will flow?

This summer, Edward and I traded candidate stories for the syllabus. Based on his suggestions, I recommend touring science fiction under an expert’s guidance. I enjoyed, for a few hours each weekend, sinking into the worlds of Ted Chiang, Ursula K. LeGuinn, N. K. Jemison, Ken Liu, and others. My scientific background informed my reading more than I’d expected. Some authors, I could tell, had researched their subjects thoroughly. When they transitioned from science into fiction, I trusted and followed them. Other authors tossed jargon into their writing but evidenced a lack of deep understanding. One author nailed technical details about quantum computation, initially impressing me, but missed the big picture: his conflict hinged on a misunderstanding about entanglement. I see all these stories as affording opportunities for learning and teaching, in different ways.

Students can begin registering for “Writing Quantum Steampunk: Science-Fiction Workshop” on October 24. We can offer only 15 seats, due to Writers’ House standards, so secure yours as soon as you can. Part of me still wonders how the Hilbert space I came to be co-teaching a quantum-steampunk creative-writing course.¹ But I look forward to reading with you next spring!

¹A Hilbert space is a mathematical object that represents a quantum system. But you needn’t know that to succeed in the course.

Always appropriate

Posted on August 11, 2024 by Nicole Yunger Halpern

I met boatloads of physicists as a master’s student at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. Researchers pass through Perimeter like diplomats through my current neighborhood—the Washington, DC area—except that Perimeter’s visitors speak math instead of legalese and hardly any of them wear ties. But Nilanjana Datta, a mathematician at the University of Cambridge, stood out. She was one of the sharpest, most on-the-ball thinkers I’d ever encountered. Also, she presented two academic talks in a little black dress.

The academic year had nearly ended, and I was undertaking research at the intersection of thermodynamics and quantum information theory for the first time. My mentors and I were applying a mathematical toolkit then in vogue, thanks to Nilanjana and colleagues of hers: one-shot quantum information theory. To explain one-shot information theory, I should review ordinary information theory. Information theory is the study of how efficiently we can perform information-processing tasks, such as sending messages over a channel.

Say I want to send you $n$ copies of a message. Into how few bits (units of information) can I compress the $n$ copies? First, suppose that the message is classical, such that a telephone could convey it. The average number of bits needed per copy equals the message’s Shannon entropy, a measure of your uncertainty about which message I’m sending. Now, suppose that the message is quantum. The average number of quantum bits needed per copy is the von Neumann entropy, now a measure of your uncertainty. At least, the answer is the Shannon or von Neumann entropy in the limit as $n$ approaches infinity. This limit appears disconnected from reality, as the universe seems not to contain an infinite amount of anything, let alone telephone messages. Yet the limit simplifies the mathematics involved and approximates some real-world problems.

But the limit doesn’t approximate every real-world problem. What if I want to send only one copy of my message—one shot? One-shot information theory concerns how efficiently we can process finite amounts of information. Nilanjana and colleagues had defined entropies beyond Shannon’s and von Neumann’s, as well as proving properties of those entropies. The field’s cofounders also showed that these entropies quantify the optimal rates at which we can process finite amounts of information.

My mentors and I were applying one-shot information theory to quantum thermodynamics. I’d read papers of Nilanjana’s and spoken with her virtually (we probably used Skype back then). When I learned that she’d visit Waterloo in June, I was a kitten looking forward to a saucer of cream.

Nilanjana didn’t disappoint. First, she presented a seminar at Perimeter. I recall her discussing a resource theory (a simple information-theoretic model) for entanglement manipulation. One often models entanglement manipulators as experimentalists who can perform local operations and classical communications: each experimentalist can poke and prod the quantum system in their lab, as well as link their labs via telephone. We abbreviate the set of local operations and classical communications as LOCC. Nilanjana broadened my view to the superset SEP, the operations that map every separable (unentangled) state to a separable state.

Kudos to John Preskill for hunting down this screenshot of the video of Nilanjana’s seminar. The author appears on the left.

Then, because she eats seminars for breakfast, Nilanjana presented an even more distinguished talk the same day: a colloquium. It took place at the University of Waterloo’s Institute for Quantum Computing (IQC), a nearly half-hour walk from Perimeter. Would I be willing to escort Nilanjana between the two institutes? I most certainly would.

Nilanjana and I arrived at the IQC auditorium before anyone else except the colloquium’s host, Debbie Leung. Debbie is a University of Waterloo professor and another of the most rigorous quantum information theorists I know. I sat a little behind the two of them and marveled. Here were two of the scions of the science I was joining. Pinch me.

My relationship with Nilanjana deepened over the years. The first year of my PhD, she hosted a seminar by me at the University of Cambridge (although I didn’t present a colloquium later that day). Afterward, I wrote a Quantum Frontiers post about her research with PhD student Felix Leditzky. The two of them introduced me to second-order asymptotics. Second-order asymptotics dictate the rate at which one-shot entropies approach standard entropies as $n$ (the number of copies of a message I’m compressing, say) grows large.

The following year, Nilanjana and colleagues hosted me at “Beyond i.i.d. in Information Theory,” an annual conference dedicated to one-shot information theory. We convened in the mountains of Banff, Canada, about which I wrote another blog post. Come to think of it, Nilanjana lies behind many of my blog posts, as she lies behind many of my papers.

But I haven’t explained about the little black dress. Nilanjana wore one when presenting at Perimeter and the IQC. That year, I concluded that pants and shorts caused me so much discomfort, I’d wear only skirts and dresses. So I stuck out in physics gatherings like a theorem in a newspaper. My mother had schooled me in the historical and socioeconomic significance of the little black dress. Coco Chanel invented the slim, simple, elegant dress style during the 1920s. It helped free women from stifling, time-consuming petticoats and corsets: a few decades beforehand, dressing could last much of the morning—and then one would change clothes for the afternoon and then for the evening. The little black dress offered women freedom of movement, improved health, and control over their schedules. Better, the little black dress could suit most activities, from office work to dinner with friends.

Yet I didn’t recall ever having seen anyone present physics in a little black dress.

I almost never use this verb, but Nilanjana rocked that little black dress. She imbued it with all the professionalism and competence ever associated with it. Also, Nilanjana had long, dark hair, like mine (although I’ve never achieved her hair’s length); and she wore it loose, as I liked to. I recall admiring the hair hanging down her back after she received a question during the IQC colloquium. She’d whirled around to write the answer on the board, in the rapid-fire manner characteristic of her intellect. If one of the most incisive scientists I knew could wear dresses and long hair, then so could I.

Felix is now an assistant professor at the University of Illinois in Urbana-Champaign. I recently spoke with him and Mark Wilde, another one-shot information theorist and a guest blogger on Quantum Frontiers. The conversation led me to reminisce about the day I met Nilanjana. I haven’t visited Cambridge in years, and my research has expanded from one-shot thermodynamics into many-body physics. But one never forgets the classics.

Building a Visceral Understanding of Quantum Phenomena

Posted on August 5, 2024 by glenevenbly

A great childhood memory that I have comes from first playing “The Incredible Machine” on PC in the early 90’s. For those not in the know, this is a physics-based puzzle game about building Rube Goldberg style contraptions to achieve given tasks. What made this game a standout for me was the freedom that it granted players. In many levels you were given a disparate set of components (e.g. strings, pulleys, rubber bands, scissors, conveyor belts, Pokie the Cat…) and it was entirely up to you to “MacGuyver” your way to some kind of solution (incidentally, my favorite TV show from that time period). In other words, it was often a creative exercise in designing your own solution, rather than “connecting the dots” to find a single intended solution. Growing up with games like this undoubtedly had significant influence in directing me to my profession as a research scientist: a job which is often about finding novel or creative solutions to a task given a limited set of tools.

From the late 90’s onwards puzzle games like “The Incredible Machine” largely went out of fashion as developers focused more on 3D games that exploited that latest hardware advances. However, this genre saw a resurgence in 2010’s spearheaded by developer “Zachtronics” who released a plethora of popular, and exceptionally challenging, logic and programming based puzzle games (some of my favorites include Opus Magnum and TIS-100). Zachtronics games similarly encouraged players to solve problems through creative designs, but also had the side-effect of helping players to develop and practice tangible programming skills (e.g. design patterns, control flow, optimization). This is a really great way to learn, I thought to myself.

So, fast-forward several years, while teaching undergraduate/graduate quantum courses at Georgia Tech I began thinking about whether it would be possible to incorporate quantum mechanics (and specifically quantum circuits) into a Zachtronics-style puzzle game. My thinking was that such a game might provide an opportunity for students to experiment with quantum through a hands-on approach, one that encouraged creativity and self-directed exploration. I was also hoping that representing quantum processes through a visual language that emphasized geometry, rather than mathematical language, could help students develop intuition in this setting. These thoughts ultimately led to the development of The Qubit Factory. At its core, this is a quantum circuit simulator with a graphic interface (not too dissimilar to the Quirk quantum circuit simulator) but providing a structured sequence of challenges, many based on tasks of real-life importance to quantum computing, that players must construct circuits to solve.

**An example level of The Qubit Factory in action, showcasing a potential solution to a task involving quantum error correction.** The column of “?” tiles represents a noisy channel that has a small chance of flipping any qubit that passes through. Players are challenged to send qubits from the input on the left to the output on the right while mitigating errors that occur due to this noisy channel. The solution shown here is based on a bit-flip code, although a more advanced strategy is required to earn a bonus star for the level!

Quantum Gamification and The Qubit Factory

My goal in designing The Qubit Factory was to provide an accurate simulation of quantum mechanics (although not necessarily a complete one), such that players could learn some authentic, working knowledge about quantum computers and how they differ from regular computers. However, I also wanted to make a game that was accessible to the layperson (i.e. without a prior knowledge of quantum mechanics or the underlying mathematical foundations like linear algebra). These goals, which are largely opposing one-another, are not easy to balance!

A key step in achieving this balance was to find a suitable visual depiction of quantum states and processes; here the Bloch sphere, which provides a simple geometric representation of qubit states, was ideal. However, it is also here that I made my first major compromise to the scope of the physics within the game by restricting the game state to real-valued wave-functions (which in turn implies that only gates which transform qubits within the X-Z plane can be allowed). I feel that this compromise was ultimately the correct choice: it greatly enhanced the visual clarity by allowing qubits to be represented as arrows on a flat disk rather than on a sphere, and similarly allowed the action of single-qubit gates to depicted clearly (i.e. as rotations and flips on the disk). Some purists may object to this limitation on grounds that it prevents universal quantum computation, but my counterpoint would be that there are still many interesting quantum tasks and algorithms that can be performed within this restricted scope. In a similar spirit, I decided to forgo the standard quantum circuit notation: instead I used stylized circuits to emphasize the geometric interpretation as demonstrated in the example below. This choice was made with the intention of allowing players to infer the action of gates from the visual design alone.

**A quantum circuit in conventional notation versus the same circuit depicted in The Qubit Factory.**

Okay, so while the Bloch sphere provides a nice way to represent (unentangled) single qubit states, we also need a way to represent entangled states of multiple qubits. Here I made use of some creative license to show entangled states as blinking through the basis states. I found this visualization to work well for conveying simple states such as the singlet state presented below, but players are also able to view the complete list of wave-function amplitudes if necessary.

$\textrm{Singlet: }\left| \psi \right\rangle = \tfrac{1}{\sqrt{2}} \left( \left| \uparrow \downarrow \right\rangle - \left| \downarrow \uparrow \right\rangle \right)$

**A singlet state is created by entangling a pair of qubits via a CNOT gate.**

Although the blinking effect is not a perfect solution for displaying superpositions, I think that it is useful in conveying key aspects like uncertainty and correlation. The animation below shows an example of the entangled wave-function collapsing when one of the qubits is measured.

A single qubit from a singlet is measured. While each qubit has a 50/50 chance of giving ▲ or ▼ when measured individually, once one qubit is measured the other qubit collapses to the anti-aligned state.

So, thus far, I have described a quantum circuit simulator with some added visual cues and animations, but how can this be turned into a game? Here, I leaned heavily on the existing example of Zachtronic (and Zachtronic-like) games: each level in The Qubit Factory provides the player with some input bits/qubits and requires the player to perform some logical task in order to produce a set of desired outputs. Some of the levels within the game are highly structured, similar to textbook exercises. They aim to teach a specific concept and may only have a narrow set of potential solutions. An example of such a structured level is the first quantum level (lvl QI.A) which tasks the player with inverting a sequence of single qubit gates. Of course, this problem would be trivial to those of you already familiar with quantum mechanics: you could use the linear algebra result $(AB)^\dag = B^\dag A^\dag$ together with the knowledge that quantum gates are unitary, so the Hermitian conjugate of each gate doubles as its inverse. But what if you didn’t know quantum mechanics, or even linear algebra? Could this problem be solved through logical reasoning alone? This is where I think that the visuals really help; players should be able to infer several key points from geometry alone:

the inverse of a flip (or mirroring about some axis) is another equal flip.
the inverse of a rotation is an equal rotation in the opposite direction.
the last transformation done on each qubit should be the first transformation to be inverted.

So I think it is plausible that, even without prior knowledge in quantum mechanics or linear algebra, a player could not only solve the level but also grasp some important concepts (i.e. that quantum gates are invertible and that the order in which they are applied matters).

**An early level challenges the player to invert the action of the 3** **gates on the left.** **A solution is given on the right, formed by composing the inverse of each gate in reverse order.**

Many of the levels in The Qubit Factory are also designed to be open-ended. Such levels, which often begin with a blank factory, have no single intended solution. The player is instead expected to use experimentation and creativity to design their own solution; this is the setting where I feel that the “game” format really shines. An example of an open-ended level is QIII.E, which gives the player 4 copies of a single qubit state $\left| \psi \right\rangle$ , guaranteed to be either the $+Z$ or $+X$ eigenstate, and tasks the player to determine which state they have been given. Those familiar with quantum computing will recognize this as a relatively simple problem in state tomography. There are many viable strategies that could be employed to solve this task (and I am not even sure of the optimal one myself). However, by circumventing the need for a mathematical calculation, the Qubit Factory allows players to easily and quickly explore different approaches. Hopefully this could allow players to find effective strategies through trial-and-error, gaining some understanding of state tomography (and why it is challenging) in the process.

**An example of a level in action! This level** **challenges the player to construct a circuit that can identify an unknown qubit state given several identical copies; a task in state tomography.** **The solution shown here uses a cascaded sequence of measurements, where the result of one measurement is used to control the axis of a subsequent measurement.**

The Qubit Factory begins with levels covering the basics of qubits, gates and measurements. It later progresses to more advanced concepts like superpositions, basis changes and entangled states. Finally it culminates with levels based on introductory quantum protocols and algorithms (including quantum error correction, state tomography, super-dense coding, quantum repeaters, entanglement distillation and more). Even if you are familiar with the aforementioned material you should still be in for a substantial challenge, so please check it out if that sounds like your thing!

The Potential of Quantum Games

I believe that interactive games have great potential to provide new opportunities for people to better understand the quantum realm (a position shared by the IQIM, members of which have developed several projects in this area). As young children, playing is how we discover the world around us and build intuition for the rules that govern it. This is perhaps a significant reason why quantum mechanics is often a challenge for new students to learn; we don’t have direct experience or intuition with the quantum world in the same way that we do with the classical world. A quote from John Preskill puts it very succinctly:

“Perhaps kids who grow up playing quantum games will acquire a visceral understanding of quantum phenomena that our generation lacks.”

The Qubit Factory can be played at www.qubitfactory.io

Quantum Frontiers

A blog by the Institute for Quantum Information and Matter @ Caltech

Category Archives: Reflections

Quantum Algorithms: A Call To Action

Technological momentum

Empowered theorists

The Challenge

Examples and non-examples

Don’t be too afraid

The first and second centuries of quantum mechanics

Lessons in frustration

Ten lessons I learned from John Preskill

Finding Ed Jaynes’s ghost

Happy 200th birthday, Carnot’s theorem!

Now published: Building Quantum Computers

Announcing the quantum-steampunk creative-writing course!

Always appropriate

Building a Visceral Understanding of Quantum Phenomena

Quantum Gamification and The Qubit Factory

The Potential of Quantum Games

Technological momentum

Empowered theorists

The Challenge

Examples and non-examples

Don’t be too afraid

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Quantum Gamification and The Qubit Factory

The Potential of Quantum Games

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