Over the last few decades, transistor density has become so high that classical computers have run into problems with some of the quirks of quantum mechanics. Quantum computers, on the other hand, exploit these quirks to revolutionize the way computers work. They promise secure communications, simulation of complex molecules, ultrafast computations, and much more. The fear of being left behind as this new technology develops is now becoming pervasive around the world. As a result, there are large, near-term investments in developing quantum technologies, with parallel efforts aimed at attracting young people into the field of quantum information science and engineering in the long-term.

I was not surprised then that, after completing my master’s thesis in quantum optics at TU Berlin in Germany, I was invited to participate in a program called Quanten 1×1 and hosted by the Junge Tueftler (Young Tinkerers) non-profit, to get young people excited about quantum technologies. As part of a small team, we decided to develop tabletop games to explain the concepts of superposition, entanglement, quantum gates, and quantum encryption. In the sections that follow, I will introduce the thought process that led to the design of one of the final products on quantum encryption. If you want to learn more about the other games, you can find the relevant links at the end of this post.

How much quantum mechanics is too much? Is it enough for people to know about the health of Schrödinger’s cat, or should we use a squishy ball with a smiley face and an arrow on it to get people excited about qubits and the Bloch sphere? In other words, what is the best way to go beyond metaphors and start delving into the real stuff? After all, we are talking about cutting-edge quantum technology here, which requires years of study to understand. Even the quantum experts I met with during the project had a hard time explaining their work to lay people.

Since there is no standardized way to explain these topics outside a university, the goal of our project was to try different models to teach quantum phenomena and make the learning as entertaining as possible. Compared to methods where people passively absorb the information, our tabletop-games approach leverages people’s curiosity and leads to active learning through trial and error.

Most of the (sensitive) information that is transmitted over the Internet is encrypted. This means that only those with the right “secret key” can unlock the digital box and read the private message within. Without the secret key used to decrypt, the message looks like gibberish – a series of random characters. To encrypt the billions of messages being exchanged every day (over 300 billion emails alone), the Internet relies heavily on public-key cryptography and so-called *one-way functions*. These mathematical functions allow one to generate a *public key* to be shared with everyone, from a *private key* kept to themselves. The public key plays the role of a digital padlock that only the private key can unlock. Anyone (human or computer) who wants to communicate with you privately can get a digital copy of your padlock (by copying it from a pinned tweet on your Twitter account, for example), put *their* private message inside a digital box provided by their favorite app or Internet communication protocol running behind the scenes, lock the digital box using *your* digital padlock (public-key), and then send it over to you (or, accidentally, to anyone else who may be trying to eavesdrop). Ingeniously, only the person with the private key (*you*) can open the box and read the message, even if everyone in the world has access to that digital box and padlock.

But there is a problem. Current one-way functions hide the private key within the public key in a way that powerful enough quantum computers can reveal. The implications of this are pretty staggering. Your information (bank account, email, bitcoin wallet, etc) as currently encrypted will be available to anyone with such a computer. This is a very serious issue of global importance. So serious indeed, that the President of the United States recently released a memo aimed at addressing this very issue. Fortunately, there are ways to fight quantum with quantum. That is, there are *quantum encryption* protocols that not even quantum computers can break. In fact, they are as secure as the laws of physics.

**Quantum Keys**

A popular way of illustrating how quantum encryption works is through single photon sources and polarization filters. In classroom settings, this often boils down to lasers and small polarizing filters a few meters apart. Although lasers are pretty cool, they emit streams of photons (particles of light), not single photons needed for quantum encryption. Moreover, measuring polarization of individual photons (another essential part of this process) is often very tricky, especially without the right equipment. In my opinion the concept of quantum mechanical measurement and the collapse of wave functions is not easily communicated in this way.

Inspired by wooden toys and puzzles my mom bought for me as a kid after visits to the dentist, I tried to look for a more physical way to visualize the experiment behind the famous BB84 quantum key distribution protocol. After a lot of back and forth between the drawing board and laser cutter, the first quantum key generator (QeyGen) was built.

*Note: This short description leaves out some details. For a deeper dive, I recommend watching the tutorial video on our Youtube channel.*

The quantum key generator (QeyGen) consists of an outer and an inner box. The outer box is used by the person generating the secret key, while the inner box is used by the person with whom they wish to share that key. The sender prepares a coin in one of two states (heads = 0, tails = 1) and inserts it either into slot 1 (horizontal basis), or slot 2 (vertical basis) of the outer box. The receiver then measures the state of the coin in one of the same two bases by sliding the inner box to the left (horizontal basis = 1) or right (vertical basis = 2). Crucially, if the bases to prepare and measure the coin match, then both sender and receiver get the same value for the coin. But if the basis used to prepare the coin doesn’t match the measurement basis, the value of the coin collapses into one of the two allowed states in the measurement basis with 50/50 chance. Because of this design, the box can be used to illustrate the BB84 protocol that allows two distant parties to create and share a secure encryption key.

The following is a step by step tutorial on how to play out the BB84 protocol with the QeyGen. You can play it with two (Alice, Bob) or three (Alice, Bob, Eve) people. It is useful to know right from the start that this protocol is not used to send private messages, but is instead used to generate a shared private key that can then be used with various encryption methods, like the one-time pad, to send secret messages.

**BB84 Protocol:**

- Alice secretly “prepares” a coin by inserting it facing-towards (0) or facing-away (1) from her into one of the two slots (bases) on the outer box. She writes down the value (0 or 1) and basis (horizontal or vertical) of the coin she just inserted.
- (optional) Eve, the eavesdropper, tries to “measure” the coin by sliding the inner box left (horizontal basis) or right (vertical basis), before putting the coin back through the outer box without anyone noticing.
- Bob then secretly measures the coin in a basis of his choice and writes down the value (0 or 1) and basis (horizontal and vertical) as well.
- Steps 1 and 3 are then repeated several times. The more times Alice and Bob go through this process, the more secure their secret key will be.

**Sharing the key while checking for eavesdroppers:**

- Alice and Bob publicly discuss which bases they used at each “prepare” and “measure” step, and cross out the values of the coin corresponding to the bases that didn’t match (about half of them on average; here, it would be rounds 1,3,5,6,7, and 11).
- Then, they publicly announce the first few (or a random subset of the) values that survive the previous step (i.e. have matching bases; here, it is rounds 2 and 4). If the values match for each round, then it is safe to assume that there was no eavesdrop attack. The remaining values are kept secret and can be used as a secure key for further communication.
- If the values of Alice and Bob don’t match, Eve must have measured the coin (before Bob) in the wrong basis (hence, randomizing its value) and put it back in the wrong orientation from the one Alice had originally chosen. Having detected Eve’s presence, Alice and Bob switch to a different channel of communication and try again.

Note that the more rounds Alice and Bob choose for the eavesdropper detection, the higher the chance that the channel of communication is secure, since N rounds that all return the same value for the coin mean a chance that Eve got lucky and guessed Alice’s inputs correctly. To put this in perspective, a 20-round check for Eve provides a 99.9999% guarantee of security. Of course, the more rounds used to check for Eve, the fewer secure bits are left for Alice and Bob to share at the end. On average, after a total of 2(N+M) rounds, with N rounds dedicated to Eve, we get an M-bit secret key.

When we play with the box, we usually encounter three main topics that we discuss with the participants.

**qm states and quantum particles**: We talk about superposition of quantum particles and draw an analogy from the coin to polarized photons.**qm measurement and basis**: We ask about the state of the coin and discuss how we actually define a state and a basis for a coin. By using the box, we emphasize that the measurement itself (in which basis the coin is observed) can directly affect the state of the coin and collapse its “wavefunction”.**BB84 protocol**: After a little playtime of preparing and measuring the coin with the box, we introduce the steps to perform the BB84 protocol as described above. The penny-dropping moment (pun intended) often happens when the participants realize that a spy intervening between preparation and measurement can change the state of the coin, leading to contradictions in the subsequent eavesdrop test of the protocol and exposing the spy.

I hope that this small outline has provided a rough idea of how the box works and why we developed it. If you have access to a laser cutter, I highly recommend making a QeyGen for yourself (link to files below). For any further questions, feel free to contact me at t.schubert@fu-berlin.de.

Project page Junge Tueftler: tueftelakademie.de/quantum1x1

Video series for the QeyGen: youtube.com/watch?v=YmdoAP1TJRo

Laser cut files: thingiverse.com/thing:5376516

*The program was funded by the Federal Ministry of Education and Research (Germany) and was a collaboration between the Jungen Tueftlern and the Technical University of Berlin.*

Captain Okoli inherited his name from Chiamaka Okoli, who was a classmate and roommate of mine while we pursued our master’s degrees at the Perimeter Institute for Theoretical Physics. Unfortunately, an illness took Chiamaka’s life shortly after she completed her PhD. Captain Okoli is my tribute to her memory, but my book lacked the space for an explanation of who Chiamaka was or how Captain Okoli got his name. The Perimeter Institute offered a platform in its publication *Inside the Perimeter*. You can find the article—a story about an innovative, daring, and kind woman—here.

Literary Hub has now published my answer.

According to its website, “Literary Hub is an organizing principle in the service of literary culture, a single, trusted, daily source for all the news, ideas and richness of contemporary literary life. There is more great literary content online than ever before, but it is scattered, easily lost—with the help of its editorial partners, Lit Hub is a site readers can rely on for smart, engaged, entertaining writing about all things books.”

My article, “Five best books about the romance of Victorian science,” appeared there last week. You’ll find fiction, nonfiction as imaginative as fiction, and crossings of the border between the two.

My contribution to literature about the romance of Victorian science—my (mostly) nonfiction book, *Quantum Steampunk: The Physics Of Yesterday’s Tomorrow*—was published two weeks ago. Where’s a hot-air-balloon emoji when you need one?

You can read more in *Quanta Magazine* here and yet more in chapter 9 of my book. For recent advances in fluctuation relations, as opposed to the broad introduction there, check out earlier *Quantum Frontiers* posts here, here, here, here, and here.

Roughly nine years later, I concede his point.

The revelation walloped me last month, as I was polishing a paper with experimental collaborators. Members of the Institute for Quantum Optics and Quantum Information (IQOQI) in Innsbruck, Austria—Florian Kranzl, Manoj Joshi, and Christian Roos—had performed an experiment in trapped-ion guru Rainer Blatt’s lab. Their work realized an experimental proposal that I’d designed with fellow theorists near the beginning of my postdoc stint. We aimed to observe signatures of particularly quantum thermalization

Throughout the universe, small systems exchange stuff with their environments. For instance, the Earth exchanges heat and light with the rest of the solar system. After exchanging stuff for long enough, the small system *equilibrates* with the environment: Large-scale properties of the small system (such as its volume and energy) remain fairly constant; and as much stuff enters the small system as leaves, on average. The Earth remains far from equilibrium, which is why we aren’t dead yet.

In many cases, in equilibrium, the small system shares properties of the environment, such as the environment’s temperature. In these cases, we say that the small system has *thermalized* and, if it’s quantum, has reached a *thermal state*.

The stuff exchanged can consist of energy, particles, electric charge, and more. Unlike classical planets, quantum systems can exchange things that participate in quantum uncertainty relations (experts: that fail to commute). Quantum uncertainty mucks up derivations of the thermal state’s mathematical form. Some of us quantum thermodynamicists discovered the mucking up—and identified exchanges of quantum-uncertain things as particularly nonclassical thermodynamics—only a few years ago. We reworked conventional thermodynamic arguments to accommodate this quantum uncertainty. The small system, we concluded, likely equilibrates to near a thermal state whose mathematical form depends on the quantum-uncertain stuff—what we termed a *non-Abelian thermal state*. I wanted to see this equilibration in the lab. So I proposed an experiment with theory collaborators; and Manoj, Florian, and Christian took a risk on us.

The experimentalists arrayed between six and fifteen ions in a line. Two ions formed the small system, and the rest formed the quantum environment. The ions exchanged the -, -, and -components of their spin angular momentum—stuff that participates in quantum uncertainty relations. The ions began with a fairly well-defined amount of each spin component, as described in another blog post. The ions exchanged stuff for a while, and then the experimentalists measured the small system’s quantum state.

The small system equilibrated to near the non-Abelian thermal state, we found. No conventional thermal state modeled the results as accurately. Score!

My postdoc and numerical-simulation wizard Aleks Lasek modeled the experiment on his computer. The small system, he found, remained farther from the non-Abelian thermal state in his simulation than in the experiment. Aleks plotted the small system’s distance to the non-Abelian thermal state against the ion chain’s length. The points produced experimentally sat lower down than the points produced numerically. Why?

I think I can explain that, I said. The two ions exchange stuff with the rest of the ions, which serve as a quantum environment. But the two ions exchange stuff also with the wider world, such as stray electromagnetic fields. The latter exchanges may push the small system farther toward equilibrium than the extra ions alone do.

Fortunately for the development of my explanatory skills, collaborators prodded me to hone my argument. The wider world, they pointed out, effectively has a very high temperature—an infinite temperature.^{1} Equilibrating with that environment, the two ions would acquire an infinite temperature themselves. The two ions would approach an infinite-temperature thermal state, which differs from the non-Abelian thermal state we aimed to observe.

Fair, I said. But the extra ions probably have a fairly high temperature themselves. So the non-Abelian thermal state is probably close to the infinite-temperature thermal state. Analogously, if someone cooks goulash similarly to his father, and the father cooks goulash similarly to his grandfather, then the youngest chef cooks goulash similarly to his grandfather. If the wider world pushes the two ions to equilibrate to infinite temperature, then, because the infinite-temperature state lies near the non-Abelian thermal state, the wider world pushes the two ions to equilibrate to near the non-Abelian thermal state.

I plugged numbers into a few equations to check that the extra ions do have a high temperature. (Perhaps I should have done so before proposing the argument above, but my collaborators were kind enough not to call me out.)

Aleks hammered the nail into the problem’s coffin by incorporating into his simulations the two ions’ interaction with an infinite-temperature wider world. His numerical data points dropped to near the experimental data points. The new plot supported my story.

*I can explain that!* Aleks’s results buoyed me the whole next day; I found myself smiling at random times throughout the afternoon. Not that I’d explained a grand mystery, like the unexpected hiss heard by Arno Penzias and Robert Wilson when they turned on a powerful antenna in 1964. The hiss turned out to come from the cosmic microwave background (CMB), a collection of photons that fill the visible universe. The CMB provided evidence for the then-controversial Big Bang theory of the universe’s origin. Discovering the CMB earned Penzias and Wilson a Nobel Prize. If the noise caused by the CMB was music to cosmologists’ ears, the noise in our experiment is the quiet wailing of a shy banshee. But it’s *our* experiment’s noise, and we understand it now.

The experience hasn’t weaned me off the romance of proving theorems about thought experiments. Theorems about thermodynamic quantum uncertainty inspired the experiment that yielded the plot that confused us. But I now second Gil’s sentiment. In the throes of an experiment, “I can explain that” can feel like a battle cry.

^{1}Experts: The wider world effectively has an infinite temperature because (i) the dominant decoherence is dephasing relative to the product eigenbasis and (ii) the experimentalists rotate their qubits often, to simulate a rotationally invariant Hamiltonian evolution. So the qubits effectively undergo dephasing relative to the , , and eigenbases.

The different fish swimming in the Koi pond are, in many ways, like charges being exchanged between subsystems. A “charge” is any globally conserved quantity. Examples of charges include energy, particles, electric charge, or angular momentum. Consider a system consisting of a cup of coffee in your office. The coffee will dynamically exchange charges with your office in the form of heat energy. Still, the total energy of the coffee and office is conserved (assuming your office walls are *really *well insulated). In this example, we had one type of charge (heat energy) and two subsystems (coffee and office). Consider now a closed system consisting of many subsystems and many different types of charges. The closed system is like the finite Koi pond with different charges like the different fish species. The charges can move around locally, but the total number of charges is globally fixed, like how the fish swim around but can’t escape the pond. Also, the presence of one type of charge can alter another’s movement, just as a big fish might block a little one’s path.

Unfortunately, the Koi pond analogy reaches its limit when we move to quantum charges. Classically, charges *commute*. This means that we can simultaneously determine the amount of each charge in our system at each given moment. In quantum mechanics, this isn’t necessarily true. In other words, classically, I can count the number of glossy fish and matt fish. But, in quantum mechanics, I can’t.

So why does this matter? Subsystems exchanging charges are prevalent in thermodynamics. Quantum thermodynamics extends thermodynamics to include small systems and quantum effects. Noncommutation underlies many important quantum phenomena. Hence, studying the exchange of noncommuting charges is pivotal in understanding quantum thermodynamics. Consequently, noncommuting charges have emerged as a rapidly growing subfield of quantum thermodynamics. Many interesting results have been discovered from no longer assuming that charges commute (such as these). Until recently, most of these discoveries have been theoretical. Bridging these discoveries to experimental reality requires Hamiltonians (functions that tell you how your system evolves in time) that move charges locally but conserve them globally. Last year it was unknown whether these Hamiltonians exist, what they look like generally, how to build them, and for what charges you could find them.

Nicole Yunger Halpern (NIST physicist, my co-advisor, and Quantum Frontiers blogger) and I developed a prescription for building Koi ponds for noncommuting charges. Our prescription allows you to systematically build Hamiltonians that overtly move noncommuting charges between subsystems while conserving the charges globally. These Hamiltonians are built using Lie algebras, abstract mathematical tools that can describe many physical quantities (including everything in the standard model of particle physics and space-time metric). Our results were recently published in *npj QI*. We hope that our prescription will bolster the efforts to bridge the results of noncommuting charges to experimental reality.

In the end, a little group theory was all I needed for my Koi pond. Maybe I’ll build a treehouse next with calculus or a remote control car with combinatorics.

]]>I was one of 50-ish physicists crammed into the lobby—and in the doorway, down the stairs, and onto the sidewalk—of a Manhattan hotel last December. Everyone had received a COVID vaccine, and the omicron variant hadn’t yet begun chewing up North America. Everyone had arrived on the same bus that evening, feeding on the neon-bright views of Fifth Avenue through dinnertime. Everyone wanted to check in and offload suitcases before experiencing firsthand the reason for the nickname “the city that never sleeps.” So everyone was jumbled together in what passed for a line.

We’d just passed the halfway point of the week during which I was pretending to be a string theorist. I do that whenever my research butts up against black holes, chaos, quantum gravity (the attempt to unify quantum physics with Einstein’s general theory of relativity), and alternative space-times. These topics fall under the heading “It from Qubit,” which calls for understanding puzzling physics (“It”) by analyzing how quantum systems process information (“Qubit”). The “It from Qubit” crowd convenes for one week each December, to share progress and collaborate.^{1} The group spends Monday through Wednesday at Princeton’s Institute for Advanced Study (IAS), dogged by photographs of Einstein, busts of Einstein, and roads named after Einstein. A bus ride later, the group spends Thursday and Friday at the Simons Foundation in New York City.

I don’t usually attend “It from Qubit” gatherings, as I’m actually a quantum information theorist and quantum thermodynamicist. Having admitted as much during the talk I presented at the IAS, I failed at pretending to be a string theorist. Happily, I adore being the most ignorant person in a roomful of experts, as the experience teaches me oodles. At lunch and dinner, I’d plunk down next to people I hadn’t spoken to and ask what they see as trending in the “It from Qubit” community.

One buzzword, I’d first picked up on shortly before the pandemic had begun (*replicas*). Having lived a frenetic life, that trend seemed to be declining. Rising buzzwords (*factorization* and *islands*), I hadn’t heard in black-hole contexts before. People were still tossing around terms from when I’d first forayed into “It from Qubit” (*scrambling* and *out-of-time-ordered correlator*), but differently from then. Five years ago, the terms identified the latest craze. Now, they sounded entrenched, as though everyone expected everyone else to know and accept their significance.

One buzzword labeled my excuse for joining the workshops: *complexity*. *Complexity* wears as many meanings as the stereotypical New Yorker wears items of black clothing. Last month, guest blogger Logan Hillberry wrote about complexity that emerges in networks such as brains and social media. To “It from Qubit,” complexity quantifies the difficulty of preparing a quantum system in a desired state. Physicists have conjectured that a certain quantum state’s complexity parallels properties of gravitational systems, such as the length of a wormhole that connects two black holes. The wormhole’s length grows steadily for a time exponentially large in the gravitational system’s size. So, to support the conjecture, researchers have been trying to prove that complexity typically grows similarly. Collaborators and I proved that it does, as I explained in my talk and as I’ll explain in a future blog post. Other speakers discussed experimental complexities, as well as the relationship between complexity and a simplified version of Einstein’s equations for general relativity.

I learned a bushel of physics, moonlighting as a string theorist that week. The gum-ball-machine lobby, though, retaught me something I’d learned long before the pandemic. Around the time I squeezed inside the hotel, a postdoc struck up a conversation with the others of us who were clogging the doorway. We had a decent fraction of an hour to fill; so we chatted about quantum thermodynamics, grant applications, and black holes. I asked what the postdoc was working on, he explained a property of black holes, and it reminded me of a property of thermodynamics. I’d nearly reached the front desk when I realized that, out of the sheer pleasure of jawing about physics with physicists in person, I no longer wanted to reach the front desk. The moment dangles in my memory like a crystal ornament from the lobby’s tree—pendant from the pandemic, a few inches from the vaccines suspended on one side and from omicron on the other. For that moment, in a lobby buoyed by holiday lights, wrapped in enough warmth that I’d forgotten the December chill outside, I belonged to the “It from Qubit” community as I hadn’t belonged to any community in 22 months.

Happy new year.

^{1}In person or virtually, pandemic-dependently.

*Thanks to the organizers of the IAS workshop—Ahmed Almheiri, Adam Bouland, Brian Swingle—for the invitation to present and to the organizers of the Simons Foundation workshop—Patrick Hayden and Matt Headrick—for the invitation to attend.*

A big surprise followed: Tom Ventsias, the director of communications at the University of Maryland Institute for Advanced Computer Studies (UMIACS), added, “I wanted to hear your thoughts about possibly doing a dual photo shoot for you—one more ‘traditional,’ one ‘quantum steampunk’ style.”

Steampunk, as *Quantum Frontiers* regulars know, is a genre of science fiction. It combines futuristic technologies, such as time machines and automata, with Victorian settings. I call my research “quantum steampunk,” as it combines the cutting-edge technology of quantum information science with the thermodynamics—the science of energy—developed during the 1800s. I’ve written a thesis called “Quantum steampunk”; authored a trade nonfiction book with the same title; and presented enough talks about quantum steampunk that, strung together, they’d give one laryngitis. But I don’t own goggles, hoop skirts, or petticoats. The most steampunk garb I’d ever donned before this autumn, I wore for a few minutes at age six or so, for dress-up photos at a theme park. I don’t even like costumes.

But I earned my PhD under the auspices of fellow *Quantum Frontiers* blogger John Preskill,^{1} whose career suggests a principle to live by: While unravelling the universe’s nature and helping to shape humanity’s intellectual future, you mustn’t take yourself too seriously. This blog has exhibited a photo of John sitting in Caltech’s information-sciences building, exuding all the gravitas of a Princeton degree, a Harvard degree, and world-impacting career—sporting a baseball glove you’d find in a high-school gym class, as though it were a Tag Heuer watch. John adores baseball, and the photographer who documented Caltech’s Institute for Quantum Information and Matter brought out the touch of whimsy like the ghost of a smile.

Let’s try it, I told Tom.

One rust-colored November afternoon, I climbed to the top of UMIACS headquarters—the Iribe Center—whose panoramic view of campus begs for photographs. Two students were talking in front of a whiteboard, and others were lunching on the sandwiches, fruit salad, and cheesecake ordered by Tom’s team. We took turns brandishing markers, gesturing meaningfully, and looking contemplative.

Then, the rest of my team dispersed, and the clock rewound 150 years.

The professionalism and creativity of Tom’s team impressed me. First, they’d purchased a steampunk hat, complete with goggles and silver wires. Recalling the baseball-glove photo, I suggested that I wear the hat while sitting at a table, writing calculations as I ordinarily would.

Then, the team upped the stakes. Earlier that week, Maria Herd, a member of the communications office, had driven me to the University of Maryland performing-arts center. We’d sifted through the costume repository until finding skirts, vests, and a poofy white shirt reminiscent of the 1800s. I swapped clothes near the photo-shoot area, while the communications team beamed a London street in from the past. Not really, but they nearly did: They’d found a backdrop suitable for the 2020 Victorian-era Netflix hit *Enola Holmes* and projected the backdrop onto a screen. I stood in front of the screen, and a sheet of glass stood in front of me. I wrote equations on the glass while the photographer, John Consoli, snapped away.

The final setup, I would never have dreamed of. Days earlier, the communications team had located an elevator lined, inside, with metal links. They’d brought colorful, neon-lit rods into the elevator and experimented with creating futuristic backdrops. On photo-shoot day, they positioned me in the back of the elevator and held the light-saber-like rods up.

But we couldn’t stop anyone from calling the elevator. We’d ride up to the third or fourth floor, and the door would open. A student would begin to step in; halt; and stare my floor-length skirt, the neon lights, and the photographer’s back.

“Feel free to get in.” John’s assistant, Gail Marie Rupert, would wave them inside. The student would shuffle inside—in most cases—and the door would close.

“What floor?” John would ask.

“Um…one.”

John would twist around, press the appropriate button, and then turn back to his camera.

Once, when the door opened, the woman who entered complimented me on my outfit. Another time, the student asked if he was really in the Iribe Center. I regard that question as evidence of success.

John Consoli took 654 photos. I found the process fascinating, as a physicist. I have a domain of expertise; and I know the feeling of searching for—working toward—*pushing* for—a theorem or a conceptual understanding that satisfies me, in that domain. John’s area of expertise differs from mine, so I couldn’t say what he was searching for. But I recognized his intent and concentration, as Gail warned him that time had run out and he then made an irritated noise, inched sideways, and stole a few more snapshots. I felt like I was seeing myself in a reflection—not in the glass I was writing on, but in another sphere of the creative life.

The communications team’s eagerness to engage in quantum steampunk—to experiment with it, to introduce it into photography, to make it their own—bowled me over. Quantum steampunk isn’t just a stack of papers by one research group; it’s a movement. Seeing a team invest its time, energy, and imagination in that movement felt like receiving a deep bow or curtsy. Thanks to the UMIACS communications office for bringing quantum steampunk to life.

^{1}Who hasn’t blogged in a while. How about it, John?

Of course, life within physics is also full of tradeoffs. My day job is as an experimentalist. I use tightly focused laser beams, known as *optical tweezers,* to levitate micrometer-sized glass spheres. I monitor a single microsphere’s motion as it undergoes collisions with air molecules, and I study the system as an environmental sensor of temperature, fluid flow, and acoustic waves; however, by night I am a computational physicist. I code simulations of interacting qubits subject to kinetic constraints, so-called *quantum cellular automata *(QCA). My QCA work started a few years ago for my Master’s degree, but my interest in the subject persists. I recently co-authored one paper summarizing the work so far and another detailing an experimental implementation.

QCA, the subject of this post, are themselves tradeoff-aware systems. To see what I mean, first consider their classical counterparts *cellular automata. *In their simplest construction, the system is a one-dimensional string of bits. Each bit takes a value of 0 or 1 (white or black). The* bitstring *changes in discrete time steps based on a simultaneously-applied local update rule: Each bit, along with its two nearest-neighbors, determine the next state of the central bit. Put another way, a bit either* flips*, i.e., changes 0 to 1 or 1 to 0, or remains unchanged over a timestep depending on the state of that bit’s local neighborhood. Thus, by choosing a particular rule, one encodes a trade off between activity (bit flips) and inactivity (bit remains unchanged). Despite their simple construction, cellular automata dynamics are diverse; they can produce fractals and encryption-quality random numbers. One rule even has the ability to run arbitrary computer algorithms, a property known as *universal computation*.

In QCA, bits are promoted to qubits. Instead of being just 0 or 1 like a bit, a qubit can be a continuous mixture of both 0 and 1, a property called *superposition*. In QCA, a qubit’s two neighbors being 0 or 1 determine whether or not it changes. For example, when in an active neighborhood configuration, a qubit can be coded to change from 0 to “0 plus 1” or from 1 to “0 minus 1”. This is already a head-scratcher, but things get even weirder. If a qubit’s neighbors are in a superposition, then the center qubit can become *entangled* with those neighbors. Entanglement correlates qubits in a way that is not possible with classical bits.

Do QCA support the emergent complexity observed in their classical cousins? What are the effects of a continuous state space, superposition, and entanglement? My colleagues and I attacked these questions by re-examining many-body physics tools through the lens of complexity science. Singing the lead, we have a workhorse of quantum and solid-state physics: *two-point correlations*. Singing harmony we have the bread-and-butter of network analysis: *complex-network measures*. The duet between the two tells the story of structured correlations in QCA dynamics.

In a bit more detail, at each QCA timestep we calculate the *mutual information* between all qubits *i* and all other qubits *j*. Doing so reveals how much there is to learn about one qubit by measuring another, including effects of quantum entanglement. Visualizing each qubit as a node, the mutual information can be depicted as weighted links between nodes: the more correlated two qubits are, the more strongly they are linked. The collection of nodes and links makes a network. Some QCA form unstructured, randomly-linked networks while others are highly structured.

Complex-network measures are designed to highlight certain structural patterns within a network. Historically, these measures have been used to study diverse networked-systems like friend groups on Facebook, biomolecule pathways in metabolism, and functional-connectivity in the brain. Remarkably, the most structured QCA networks we observed quantitatively resemble those of the complex systems just mentioned despite their simple construction and quantum unitary dynamics.

What’s more, the particular QCA that generate the most complex networks are those that balance the activity-inactivity trade-off. From this observation, we formulate what we call the *Goldilocks principle:* QCA that generate the most complexity are those that change a qubit if and only if the qubit’s neighbors contain an equal number of 1’s and 0’s. The Goldilocks rules are neither too inactive nor too active, balancing the tradeoff to be “*just right*.” We demonstrated the Goldilocks principle for QCA with nearest-neighbor constraints as well as QCA with nearest-and-next-nearest-neighbor constraints.

To my delight, the scientific conclusions of my QCA research resonate with broader lessons-learned from my time as a PhD student: Life is full of trade-offs, and finding the right balance is key to achieving that “just right” feeling.

]]>The Charles River separates Cambridge from Boston, at whose Logan Airport I’d arrived with a suitcase just under the societal size limit and ideas that I hoped weren’t. But as the metro car juddered onto the Longfellow Bridge, all physics papers vanished from my mind. So did concerns about how I’d find my new apartment, how much I had to accomplish before night fell (buy breakfast ingredients, retrieve boxes I’d shipped, unpack, …), and how strongly I smelled like airplane fuel.

The Charles stretched below us, sparkling with silver threads embroidered in blue, a carpet too grand for a king. On the river bobbed boats that resembled toys, their sails smaller than my paper. Boston’s skyline framed the river’s right-hand side, and Cambridge’s skyline framed the left. And what skylines they were—filled with glass and red brick; with rectangles, trapezoids, hemispheres, and turrets. I felt blessed for such a welcome to a new Cantab.

I vowed that afternoon that, every time I crossed the Charles via metro in the next three years, I’d stop reading my paper, or drafting my email, or planning my next talk. I’d look up through a window, recall the river’s beauty, and feel grateful—grateful for the privilege of living nearby and in an intellectual hub that echoes across centuries; for the freedom to pursue the ideas I dream up; and for the ability to perceive the beauty before me.

Humans have a knack for accustoming themselves to gifts. One day, we’re reveling over an acceptance letter or the latest Apple product; a year later, we’re chasing the next acceptance or cursing technology’s slowness. But an “attitude of gratitude,” as my high-school physics teacher put it, enhances our relationships, our health, and our satisfaction with life. I’m grateful for the nudge that, whenever I traveled to or from home throughout the past three years, reminded me to feel grateful.

I wish you a Charles River, this season and every season.

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