# Memories of things past

My best friend—who’s held the title of best friend since kindergarten—calls me the keeper of her childhood memories. I recall which toys we played with, the first time I visited her house,1 and which beverages our classmates drank during snack time in kindergarten.2 She wouldn’t be surprised to learn that the first workshop I’ve co-organized centered on memory.

Memory—and the loss of memory—stars in thermodynamics. As an example, take what my husband will probably do this evening: bake tomorrow’s breakfast. I don’t know whether he’ll bake fruit-and-oat cookies, banana muffins, pear muffins, or pumpkin muffins. Whichever he chooses, his baking will create a scent. That scent will waft across the apartment, seep into air vents, and escape into the corridor—will disperse into the environment. By tomorrow evening, nobody will be able to tell by sniffing what my husband will have baked.

That is, the kitchen’s environment lacks a memory. This lack contributes to our experience of time’s arrow: We sense that time passes partially by smelling less and less of breakfast. Physicists call memoryless systems and processes Markovian.

Our kitchen’s environment is Markovian because it’s large and particles churn through it randomly. But not all environments share these characteristics. Metaphorically speaking, a dispersed memory of breakfast may recollect, return to a kitchen, and influence the following week’s baking. For instance, imagine an atom in a quantum computer, rather than a kitchen in an apartment. A few other atoms may form our atom’s environment. Quantum information may leak from our atom into that environment, swish around in the environment for a time, and then return to haunt our atom. We’d call the atom’s evolution and environment non-Markovian.

I had the good fortune to co-organize a workshop about non-Markovianity—about memory—this February. The workshop took place at the Banff International Research Station, abbreviated BIRS, which you pronounce like the plural of what you say when shivering outdoors in Canada. BIRS operates in the Banff Centre for Arts and Creativity, high in the Rocky Mountains. The Banff Centre could accompany a dictionary entry for pristine, to my mind. The air feels crisp, the trees on nearby peaks stand out against the snow like evergreen fringes on white velvet, and the buildings balance a rustic-mountain-lodge style with the avant-garde.

The workshop balanced styles, too, but skewed toward the theoretical and abstract. We learned about why the world behaves classically in our everyday experiences; about information-theoretic measures of the distances between quantum states; and how to simulate, on quantum computers, chemical systems that interact with environments. One talk, though, brought our theory back down to (the snow-dusted) Earth.

Gabriela Schlau-Cohen runs a chemistry lab at MIT. She wants to understand how plants transport energy. Energy arrives at a plant from the sun in the form of light. The light hits a pigment-and-protein complex. If the plant is lucky, the light transforms into a particle-like packet of energy called an exciton. The exciton traverses the receptor complex, then other complexes. Eventually, the exciton finds a spot where it can enable processes such as leaf growth.

A high fraction of the impinging photons—85%—transform into excitons. How do plants convert and transport energy as efficiently as they do?

Gabriela’s group aims to find out—not by testing natural light-harvesting complexes, but by building complexes themselves. The experimentalists mimic the complex’s protein using DNA. You can fold DNA into almost any shape you want, by choosing the DNA’s base pairs (basic units) adroitly and by using “staples” formed from more DNA scraps. The sculpted molecules are called DNA origami.

Gabriela’s group engineers different DNA structures, analogous to complexes’ proteins, to have different properties. For instance, the experimentalists engineer rigid structures and flexible structures. Then, the group assesses how energy moves through each structure. Each structure forms an environment that influences excitons’ behaviors, similarly to how a memory-containing environment influences an atom.

The Banff environment influenced me, stirring up memories like powder displaced by a skier on the slopes above us. I first participated in a BIRS workshop as a PhD student, and then I returned as a postdoc. Now, I was co-organizing a workshop to which I brought a PhD student of my own. Time flows, as we’re reminded while walking down the mountain from the Banff Centre into town: A cemetery borders part of the path. Time flows, but we belong to that thermodynamically remarkable class of systems that retain memories…memories and a few other treasures that resist change, such as friendships held since kindergarten.

1Plushy versions of Simba and Nala from The Lion King. I remain grateful to her for letting me play at being Nala.

2I’d request milk, another kid would request apple juice, and everyone else would request orange juice.

# A (quantum) complex legacy: Part deux

I didn’t fancy the research suggestion emailed by my PhD advisor.

A 2016 email from John Preskill led to my publishing a paper about quantum complexity in 2022, as I explained in last month’s blog post. But I didn’t explain what I thought of his email upon receiving it.

It didn’t float my boat. (Hence my not publishing on it until 2022.)

The suggestion contained ingredients that ordinarily would have caulked any cruise ship of mine: thermodynamics, black-hole-inspired quantum information, and the concept of resources. John had forwarded a paper drafted by Stanford physicists Adam Brown and Lenny Susskind. They act as grand dukes of the community sussing out what happens to information swallowed by black holes.

We’re not sure how black holes work. However, physicists often model a black hole with a clump of particles squeezed close together and so forced to interact with each other strongly. The interactions entangle the particles. The clump’s quantum state—let’s call it $| \psi(t) \rangle$—grows not only complicated with time ($t$), but also complex in a technical sense: Imagine taking a fresh clump of particles and preparing it in the state $| \psi(t) \rangle$ via a sequence of basic operations, such as quantum gates performable with a quantum computer. The number of basic operations needed is called the complexity of $| \psi(t) \rangle$. A black hole’s state has a complexity believed to grow in time—and grow and grow and grow—until plateauing.

This growth echoes the second law of thermodynamics, which helps us understand why time flows in only one direction. According to the second law, every closed, isolated system’s entropy grows until plateauing.1 Adam and Lenny drew parallels between the second law and complexity’s growth.

The less complex a quantum state is, the better it can serve as a resource in quantum computations. Recall, as we did last month, performing calculations in math class. You needed clean scratch paper on which to write the calculations. So does a quantum computer. “Scratch paper,” to a quantum computer, consists of qubits—basic units of quantum information, realized in, for example, atoms or ions. The scratch paper is “clean” if the qubits are in a simple, unentangled quantum state—a low-complexity state. A state’s greatest possible complexity, minus the actual complexity, we can call the state’s uncomplexity. Uncomplexity—a quantum state’s blankness—serves as a resource in quantum computation.

Manny Knill and Ray Laflamme realized this point in 1998, while quantifying the “power of one clean qubit.” Lenny arrived at a similar conclusion while reasoning about black holes and firewalls. For an introduction to firewalls, see this blog post by John. Suppose that someone—let’s call her Audrey—falls into a black hole. If it contains a firewall, she’ll burn up. But suppose that someone tosses a qubit into the black hole before Audrey falls. The qubit kicks the firewall farther away from the event horizon, so Audrey will remain safe for longer. Also, the qubit increases the uncomplexity of the black hole’s quantum state. Uncomplexity serves as a resource also to Audrey.

A resource is something that’s scarce, valuable, and useful for accomplishing tasks. Different things qualify as resources in different settings. For instance, imagine wanting to communicate quantum information to a friend securely. Entanglement will serve as a resource. How can we quantify and manipulate entanglement? How much entanglement do we need to perform a given communicational or computational task? Quantum scientists answer such questions with a resource theory, a simple information-theoretic model. Theorists have defined resource theories for entanglement, randomness, and more. In many a blog post, I’ve eulogized resource theories for thermodynamic settings. Can anyone define, Adam and Lenny asked, a resource theory for quantum uncomplexity?

By late 2016, I was a quantum thermodynamicist, I was a resource theorist, and I’d just debuted my first black-hole–inspired quantum information theory. Moreover, I’d coauthored a review about the already-extant resource theory that looked closest to what Adam and Lenny sought. Hence John’s email, I expect. Yet that debut had uncovered reams of questions—questions that, as a budding physicist heady with the discovery of discovery, I could own. Why would I answer a question of someone else’s instead?

So I thanked John, read the paper draft, and pondered it for a few days. Then, I built a research program around my questions and waited for someone else to answer Adam and Lenny.

Three and a half years later, I was still waiting. The notion of uncomplexity as a resource had enchanted the black-hole-information community, so I was preparing a resource-theory talk for a quantum-complexity workshop. The preparations set wheels churning in my mind, and inspiration struck during a long walk.2

After watching my workshop talk, Philippe Faist reached out about collaborating. Philippe is a coauthor, a friend, and a fellow quantum thermodynamicist and resource theorist. Caltech’s influence had sucked him, too, into the black-hole community. We Zoomed throughout the pandemic’s first spring, widening our circle to include Teja Kothakonda, Jonas Haferkamp, and Jens Eisert of Freie University Berlin. Then, Anthony Munson joined from my nascent group in Maryland. Physical Review A published our paper, “Resource theory of quantum uncomplexity,” in January.

The next four paragraphs, I’ve geared toward experts. An agent in the resource theory manipulates a set of $n$ qubits. The agent can attempt to perform any gate $U$ on any two qubits. Noise corrupts every real-world gate implementation, though. Hence the agent effects a gate chosen randomly from near $U$. Such fuzzy gates are free. The agent can’t append or discard any system for free: Appending even a maximally mixed qubit increases the state’s uncomplexity, as Knill and Laflamme showed.

Fuzzy gates’ randomness prevents the agent from mapping complex states to uncomplex states for free (with any considerable probability). Complexity only grows or remains constant under fuzzy operations, under appropriate conditions. This growth echoes the second law of thermodynamics.

We also defined operational tasks—uncomplexity extraction and expenditure analogous to work extraction and expenditure. Then, we bounded the efficiencies with which the agent can perform these tasks. The efficiencies depend on a complexity entropy that we defined—and that’ll star in part trois of this blog-post series.

Now, I want to know what purposes the resource theory of uncomplexity can serve. Can we recast black-hole problems in terms of the resource theory, then leverage resource-theory results to solve the black-hole problem? What about problems in condensed matter? Can our resource theory, which quantifies the difficulty of preparing quantum states, merge with the resource theory of magic, which quantifies that difficulty differently?

I don’t regret having declined my PhD advisor’s recommendation six years ago. Doing so led me to explore probability theory and measurement theory, collaborate with two experimental labs, and write ten papers with 21 coauthors whom I esteem. But I take my hat off to Adam and Lenny for their question. And I remain grateful to the advisor who kept my goals and interests in mind while checking his email. I hope to serve Anthony and his fellow advisees as well.

1…en route to obtaining a marriage license. My husband and I married four months after the pandemic throttled government activities. Hours before the relevant office’s calendar filled up, I scored an appointment to obtain our license. Regarding the metro as off-limits, my then-fiancé and I walked from Cambridge, Massachusetts to downtown Boston for our appointment. I thank him for enduring my requests to stop so that I could write notes.

2At least, in the thermodynamic limit—if the system is infinitely large. If the system is finite-size, its entropy grows on average.

# A (quantum) complex legacy

Early in the fourth year of my PhD, I received a most John-ish email from John Preskill, my PhD advisor. The title read, “thermodynamics of complexity,” and the message was concise the way that the Amazon River is damp: “Might be an interesting subject for you.”

Below the signature, I found a paper draft by Stanford physicists Adam Brown and Lenny Susskind. Adam is a Brit with an accent and a wit to match his Oxford degree. Lenny, known to the public for his books and lectures, is a New Yorker with an accent that reminds me of my grandfather. Before the physicists posted their paper online, Lenny sought feedback from John, who forwarded me the email.

The paper concerned a confluence of ideas that you’ve probably encountered in the media: string theory, black holes, and quantum information. String theory offers hope for unifying two physical theories: relativity, which describes large systems such as our universe, and quantum theory, which describes small systems such as atoms. A certain type of gravitational system and a certain type of quantum system participate in a duality, or equivalence, known since the 1990s. Our universe isn’t such a gravitational system, but never mind; the duality may still offer a toehold on a theory of quantum gravity. Properties of the gravitational system parallel properties of the quantum system and vice versa. Or so it seemed.

The gravitational system can have two black holes linked by a wormhole. The wormhole’s volume can grow linearly in time for a time exponentially long in the black holes’ entropy. Afterward, the volume hits a ceiling and approximately ceases changing. Which property of the quantum system does the wormhole’s volume parallel?

Envision the quantum system as many particles wedged close together, so that they interact with each other strongly. Initially uncorrelated particles will entangle with each other quickly. A quantum system has properties, such as average particle density, that experimentalists can measure relatively easily. Does such a measurable property—an observable of a small patch of the system—parallel the wormhole volume? No; such observables cease changing much sooner than the wormhole volume does. The same conclusion applies to the entanglement amongst the particles.

What about a more sophisticated property of the particles’ quantum state? Researchers proposed that the state’s complexity parallels the wormhole’s volume. To grasp complexity, imagine a quantum computer performing a computation. When performing computations in math class, you needed blank scratch paper on which to write your calculations. A quantum computer needs the quantum equivalent of blank scratch paper: qubits (basic units of quantum information, realized, for example, as atoms) in a simple, unentangled, “clean” state. The computer performs a sequence of basic operations—quantum logic gates—on the qubits. These operations resemble addition and subtraction but can entangle the qubits. What’s the minimal number of basic operations needed to prepare a desired quantum state (or to “uncompute” a given state to the blank state)? The state’s quantum complexity.1

Quantum complexity has loomed large over multiple fields of physics recently: quantum computing, condensed matter, and quantum gravity. The latter, we established, entails a duality between a gravitational system and a quantum system. The quantum system begins in a simple quantum state that grows complicated as the particles interact. The state’s complexity parallels the volume of a wormhole in the gravitational system, according to a conjecture.2

The conjecture would hold more water if the quantum state’s complexity grew similarly to the wormhole’s volume: linearly in time, for a time exponentially large in the quantum system’s size. Does the complexity grow so? The expectation that it does became the linear-growth conjecture.

Evidence supported the conjecture. For instance, quantum information theorists modeled the quantum particles as interacting randomly, as though undergoing a quantum circuit filled with random quantum gates. Leveraging probability theory,3 the researchers proved that the state’s complexity grows linearly at short times. Also, the complexity grows linearly for long times if each particle can store a great deal of quantum information. But what if the particles are qubits, the smallest and most ubiquitous unit of quantum information? The question lingered for years.

Jonas Haferkamp, a PhD student in Berlin, dreamed up an answer to an important version of the question.4 I had the good fortune to help formalize that answer with him and members of his research group: master’s student Teja Kothakonda, postdoc Philippe Faist, and supervisor Jens Eisert. Our paper, published in Nature Physics last year, marked step one in a research adventure catalyzed by John Preskill’s email 4.5 years earlier.

Imagine, again, qubits undergoing a circuit filled with random quantum gates. That circuit has some architecture, or arrangement of gates. Slotting different gates into the architecture effects different transformations5 on the qubits. Consider the set of all transformations implementable with one architecture. This set has some size, which we defined and analyzed.

What happens to the set’s size if you add more gates to the circuit—let the particles interact for longer? We can bound the size’s growth using the mathematical toolkits of algebraic geometry and differential topology. Upon bounding the size’s growth, we can bound the state’s complexity. The complexity, we concluded, grows linearly in time for a time exponentially long in the number of qubits.

Our result lends weight to the complexity-equals-volume hypothesis. The result also introduces algebraic geometry and differential topology into complexity as helpful mathematical toolkits. Finally, the set size that we bounded emerged as a useful concept that may elucidate circuit analyses and machine learning.

John didn’t have machine learning in mind when forwarding me an email in 2017. He didn’t even have in mind proving the linear-growth conjecture. The proof enables step two of the research adventure catalyzed by that email: thermodynamics of quantum complexity, as the email’s title stated. I’ll cover that thermodynamics in its own blog post. The simplest of messages can spin a complex legacy.

The links provided above scarcely scratch the surface of the quantum-complexity literature; for a more complete list, see our paper’s bibliography. For a seminar about the linear-growth paper, see this video hosted by Nima Lashkari’s research group.

1The term complexity has multiple meanings; forget the rest for the purposes of this article.

2According to another conjecture, the quantum state’s complexity parallels a certain space-time region’s action. (An action, in physics, isn’t a motion or a deed or something that Hamlet keeps avoiding. An action is a mathematical object that determines how a system can and can’t change in time.) The first two conjectures snowballed into a paper entitled “Does complexity equal anything?” Whatever it parallels, complexity plays an important role in the gravitational–quantum duality.

3Experts: Such as unitary $t$-designs.

4Experts: Our work concerns quantum circuits, rather than evolutions under fixed Hamiltonians. Also, our work concerns exact circuit complexity, the minimal number of gates needed to prepare a state exactly. A natural but tricky extension eluded us: approximate circuit complexity, the minimal number of gates needed to approximate the state.

5Experts: Unitary operators.

# Eight highlights from publishing a science book for the general public

What’s it like to publish a book?

I’ve faced the question again and again this year, as my book Quantum Steampunk hit bookshelves in April. Two responses suggest themselves.

On the one hand, I channel the Beatles: It’s a hard day’s night. Throughout the publication process, I undertook physics research full-time. Media opportunities squeezed themselves into the corners of the week: podcast and radio-show recordings, public-lecture preparations, and interviews with journalists. After submitting physics papers to coauthors and journals, I drafted articles for Quanta Magazine, Literary Hub, the New Scientist newsletter, and other venues—then edited the articles, then edited them again, and then edited them again. Often, I apologized to editors about not having the freedom to respond to their comments till the weekend. Before public-lecture season hit, I catalogued all the questions that I imagined anyone might ask, and I drafted answers. The resulting document spans 16 pages, and I study it before every public lecture and interview.

Answer number two: Publishing a book is like a cocktail of watching the sun rise over the Pacific from Mt. Fuji, taking off in an airplane for the first time, and conducting a symphony in Carnegie Hall.1 I can scarcely believe that I spoke in the Talks at Google lecture series—a series that’s hosted Tina Fey, Noam Chomsky, and Andy Weir! And I found my book mentioned in the Boston Globe! And in a Dutch science publication! If I were an automaton from a steampunk novel, the publication process would have wound me up for months.

Publishing a book has furnished my curiosity cabinet of memories with many a seashell, mineral, fossil, and stuffed crocodile. Since you’ve asked, I’ll share eight additions that stand out.

1) I guest-starred on a standup-comedy podcast. Upon moving into college, I received a poster entitled 101 Things to Do Before You Graduate from Dartmouth. My list of 101 Things I Never Expected to Do in a Physics Career include standup comedy.2 I stand corrected.

Comedian Anthony Jeannot bills his podcast Highbrow Drivel as consisting of “hilarious conversations with serious experts.” I joined him and guest comedienne Isabelle Farah in a discussion about film studies, lunch containers, and hippies, as well as quantum physics. Anthony expected me to act as the straight man, to my relief. That said, after my explanation of how quantum computers might help us improve fertilizer production and reduce global energy consumption, Anthony commented that, if I’d been holding a mic, I should have dropped it. I cherish the memory despite having had to look up the term mic drop when the recording ended.

2) I met Queen Victoria. In mid-May, I arrived in Canada to present about my science and my book at the University of Toronto. En route to the physics department, I stumbled across the Legislative Assembly of Ontario. Her Majesty was enthroned in front of the intricate sandstone building constructed during her reign. She didn’t acknowledge me, of course. But I hope she would have approved of the public lecture I presented about physics that blossomed during her era.

3) You sent me your photos of Quantum Steampunk. They arrived through email, Facebook, Twitter, text, and LinkedIn. They showed you reading the book, your pets nosing it, steampunk artwork that you’d collected, and your desktops and kitchen counters. The photographs have tickled and surprised me, although I should have expected them, upon reflection: Quantum systems submit easily to observation by their surroundings.3 Furthermore, people say that art—under which I classify writing—fosters human connection. Little wonder, then, that quantum physics and writing intersect in shared book selfies.

4) A great-grandson of Ludwig Boltzmann’s emailed. Boltzmann, a 19th-century Austrian physicist, helped mold thermodynamics and its partner discipline statistical mechanics. So I sat up straighter upon opening an email from a physicist descended from the giant. Said descendant turned out to have watched a webinar I’d presented for the magazine Physics Today. Although time machines remain in the domain of steampunk fiction, they felt closer to reality that day.

5) An experiment bore out a research goal inspired by the book. My editors and I entitled the book’s epilogue Where to next? The future of quantum steampunk. The epilogue spurred me to brainstorm about opportunities and desiderata—literally, things desired. Where did I want for quantum thermodynamics to head? I shared my brainstorming with an experimentalist later that year. We hatched a project, whose experiment concluded this month. I’ll leave the story for after the paper debuts, but I can say for now that the project gives me chills—in a good way.

6) I recited part of Edgar Allan Poe’s “The Raven” with a fellow physicist at a public lecture. The Harvard Science Book Talks form a lecture series produced by the eponymous university and bookstore. I presented a talk hosted by Jacob Barandes—a Harvard physics lecturer, the secret sauce behind the department’s graduate program, and an all-around exemplar of erudition. He asked how entropy relates to “The Raven.”

For the full answer, see chapter 11 of my book. Briefly: Many entropies exist. They quantify the best efficiencies with which we can perform thermodynamic tasks such as running an engine. Different entropies can quantify different tasks’ efficiencies if the systems are quantum, otherwise small, or far from equilibrium—outside the purview of conventional 19th-century thermodynamics. Conventional thermodynamics describes many-particle systems, such as factory-scale steam engines. We can quantify conventional systems’ efficiencies using just one entropy: the thermodynamic entropy that you’ve probably encountered in connection with time’s arrow. How does this conventional entropy relate to the many quantum entropies? Imagine starting with a quantum system, then duplicating it again and again, until accruing infinitely many copies. The copies’ quantum entropies converge (loosely speaking), collapsing onto one conventional-looking entropy. The book likens this collapse to a collapse described in “The Raven”:

The speaker is a young man who’s startled, late one night, by a tapping sound. The tapping exacerbates his nerves, which are on edge due to the death of his love: “Deep into that darkness peering, long I stood there wondering, fearing, / Doubting, dreaming dreams no mortal ever dared to dream before.” The speaker realizes that the tapping comes from the window, whose shutter he throws open. His wonders, fears, doubts, and dreams collapse onto a bird’s form as a raven steps inside. So do the many entropies collapse onto one entropy as the system under consideration grows infinitely large. We could say, instead, that the entropies come to equal each other, but I’d rather picture “The Raven.”

I’d memorized the poem in high school but never had an opportunity to recite it for anyone—and it’s a gem to declaim. So I couldn’t help reciting a few stanzas in response to Jacob. But he turned out to have memorized the poem, too, and responded with the next several lines! Even as a physicist, I rarely have the chance to reach such a pinnacle of nerdiness.

7) I stumbled across a steam-driven train in Pittsburgh. Even before self-driving cars heightened the city’s futuristic vibe, Pittsburgh has been as steampunk as the Nautilus. Captains of industry (or robber barons, if you prefer) raised the city on steel that fed the Industrial Revolution.4 And no steampunk city would deserve the title without a Victorian botanical garden.

A Victorian botanical garden features in chapter 5 of my book. To see a real-life counterpart, visit the Phipps Conservatory. A poem in glass and aluminum, the Phipps opened in 1893 and even boasts a Victoria Room.

I sneaked into the Phipps during the Pittsburgh Quantum Institute’s annual conference, where I was to present a public lecture about quantum steampunk. Upon reaching the sunken garden, I stopped in my tracks. Yards away stood a coal-black, 19th-century steam train.

At least, an imitation train stood yards away. The conservatory had incorporated Monet paintings into its scenery during a temporary exhibition. Amongst the palms and ponds were arranged props inspired by the paintings. Monet painted The Gare Saint-Lazare: Arrival of a Train near a station, so a miniature train stood behind a copy of the artwork. The scene found its way into my public lecture—justifying my playing hooky from the conference for a couple of hours (I was doing research for my talk!).

My book’s botanical garden houses hummingbirds, wildebeests, and an artificial creature called a Yorkicockasheepapoo. I can’t promise that you’ll spy Yorkicockasheepapoos while wandering the Phipps, but send me a photo if you do.

8) My students and postdocs presented me with a copy of Quantum Steampunk that they’d signed. They surprised me one afternoon, shortly after publication day, as I was leaving my office. The gesture ranks as one of the most adorable things that’ve ever happened to me, and their book is now the copy that I keep on campus.

Students…book-selfie photographers…readers halfway across the globe who drop a line…People have populated my curiosity cabinet of with some of the most extraordinary book-publication memories. Thanks for reading, and thanks for sharing.

1Or so I imagine, never having watched the sun rise from Mt. Fuji or conducted any symphony, let alone one at Carnegie Hall, and having taken off in a plane for the first time while two months old.

3This ease underlies the difficulty of quantum computing: Any stray particle near a quantum computer can “observe” the computer—interact with the computer and carry off a little of the information that the computer is supposed to store.

4The Pittsburgh Quantum Institute includes Carnegie Mellon University, which owes its name partially to captain of industry Andrew Carnegie.

# Announcing the quantum-steampunk short-story contest!

The year I started studying calculus, I took the helm of my high school’s literary magazine. Throughout the next two years, the editorial board flooded campus with poetry—and poetry contests. We papered the halls with flyers, built displays in the library, celebrated National Poetry Month, and jerked students awake at morning assembly (hitherto known as the quiet kid you’d consult if you didn’t understand the homework, I turned out to have a sense of humor and a stage presence suited to quoting from that venerated poet Dr. Seuss.1 Who’d’ve thought?). A record number of contest entries resulted.

That limb of my life atrophied in college. My college—a stereotypical liberal-arts affair complete with red bricks—boasted a literary magazine. But it also boasted English and comparative-literature majors. They didn’t need me, I reasoned. The sun ought to set on my days of engineering creative-writing contests.

I’m delighted to be eating my words, in announcing the Quantum-Steampunk Short-Story Contest.

The Maryland Quantum-Thermodynamics Hub is running the contest this academic year. I’ve argued that quantum thermodynamics—my field of research—resembles the literary and artistic genre of steampunk. Steampunk stories combine Victorian settings and sensibilities with futuristic technologies, such as dirigibles and automata. Quantum technologies are cutting-edge and futuristic, whereas thermodynamics—the study of energy—developed during the 1800s. Inspired by the first steam engines, thermodynamics needs retooling for quantum settings. That retooling is quantum thermodynamics—or, if you’re feeling whimsical (as every physicist should), quantum steampunk.

The contest opens this October and closes on January 15, 2023. Everyone aged 13 or over may enter a story, written in English, of up to 3,000 words. Minimal knowledge of quantum theory is required; if you’ve heard of Schrödinger’s cat, superpositions, or quantum uncertainty, you can pull out your typewriter and start punching away.

Entries must satisfy two requirements: First, stories must be written in a steampunk style, including by taking place at least partially during the 1800s. Transport us to Meiji Japan; La Belle Époque in Paris; gritty, smoky Manchester; or a camp of immigrants unfurling a railroad across the American west. Feel free to set your story partially in the future; time machines are welcome.

Second, each entry must feature at least one quantum technology, real or imagined. Real and under-construction quantum technologies include quantum computers, communication networks, cryptographic systems, sensors, thermometers, and clocks. Experimentalists have realized quantum engines, batteries, refrigerators, and teleportation, too. Surprise us with your imagined quantum technologies (and inspire our next research-grant proposals).

In an upgrade from my high-school days, we’ll be awarding $4,500 worth of Visa gift certificates. The grand prize entails$1,500. Entries can also win in categories to be finalized during the judging process; I anticipate labels such as Quantum Technology We’d Most Like to Have, Most Badass Steampunk Hero/ine, Best Student Submission, and People’s Choice Award.

Our judges run the gamut from writers to quantum physicists. Judge Ken Liu‘s latest novel peered out from a window of my local bookstore last month. He’s won Hugo, Nebula, and World Fantasy Awards—the topmost three prizes that pop up if you google “science-fiction awards.” Appropriately for a quantum-steampunk contest, Ken has pioneered the genre of silkpunk, “a technology aesthetic based on a science fictional elaboration of traditions of engineering in East Asia’s classical antiquity.”

Emily Brandchaft Mitchell is an Associate Professor of English at the University of Maryland. She’s authored a novel and published short stories in numerous venues. Louisa Gilder wrote one of the New York Times 100 Notable Books of 2009, The Age of Entanglement. In it, she imagines conversations through which scientists came to understand the core of this year’s Nobel Prize in physics. Jeffrey Bub is a philosopher of physics and a Distinguished University Professor Emeritus at the University of Maryland. He’s also published graphic novels about special relativity and quantum physics with his artist daughter.

Patrick Warfield, a musicologist, serves as the Associate Dean for Arts and Programming at the University of Maryland. (“Programming” as in “activities,” rather than as in “writing code,” the meaning I encounter more often.) Spiros Michalakis is a quantum mathematician and the director of Caltech’s quantum outreach program. You may know him as a scientific consultant for Marvel Comics films.

Walter E. Lawrence III is a theoretical quantum physicist and a Professor Emeritus at Dartmouth College. As department chair, he helped me carve out a niche for myself in physics as an undergrad. Jack Harris, an experimental quantum physicist, holds a professorship at Yale. His office there contains artwork that features dragons.

University of Maryland undergraduate Hannah Kim designed the ad above. She and Jade LeSchack, founder of the university’s Undergraduate Quantum Association, round out the contest’s leadership team. We’re standing by for your submissions through—until the quantum internet exists—the hub’s website. Send us something to dream on.

This contest was made possible through the support of Grant 62422 from the John Templeton Foundation.

1Come to think of it, Seuss helped me prepare for a career in physics. He coined the terms wumbus and nerd; my PhD advisor invented NISQ, the name for a category of quantum devices. NISQ now has its own Wikipedia page, as does nerd

# We’re founding a quantum-thermodynamics hub!

We’re building a factory in Maryland.

It’ll tower over the University of Maryland campus, a behemoth of 19th-century brick and 21st-century glass across from the football field. Turbines will turn, and gears will grind, where students now sip lattes near the Stadium Drive parking lot. The factory’s fuel: steam, quantum physics, and ambition. Its goal: to create an epicenter for North American quantum thermodynamics.

The factory is metaphorical, of course. Collaborators and I are establishing a quantum-thermodynamics hub centered at the University of Maryland. The hub is an abstraction—a community that’ll collaborate on research, coordinate gatherings, host visitors, and raise the public’s awareness of quantum thermodynamics. But I’d rather envision the hub as a steampunk factory that pumps out discoveries and early-career scientists.

Quantum thermodynamics has burgeoned over the past decade, especially in Europe. At the beginning of my PhD, I read paper after paper that acknowledged COST, a funding agency established by the European Union. COST dedicated a grant to thermodynamics guided by the mathematics and concepts of quantum information theory. The grant funded students, travel, and the first iterations of an annual conference that continues today. Visit Germany, Finland, France, Britain (which belonged to the European Union when I began my PhD), or elsewhere across the pond, and you’ll stumble across quantum-thermodynamics strongholds. Hotspots burn also in Brazil, Israel, Singapore, and elsewhere.

Inspired by our international colleagues, collaborators and I are banding together. Since I founded a research group last year, Maryland has achieved a critical mass of quantum thermodynamicists: Chris Jarzynski reigns as a king of the field of fluctuation relations, equalities that help us understand why time flows in only one direction. Sebastian Deffner, I regard as an academic older brother to look up to. And I run the Quantum-Steampunk Laboratory.

We’ve built railroads to research groups across the continent and steamers to cross the ocean. Other members of the hub include Kanu Sinha, a former Marylander who studies open systems in Arizona; Steve Campbell, a Dublin-based prover of fundamental bounds; and two experts on quantum many-body systems: former Marylander Amir Kalev and current Marylander Luis Pedro García-Pintos. We’re also planning collaborations with institutions from Canada to Vienna.

The hub will pursue a threefold mission of research, community building, and outreach. As detailed on our research webpage, “We aim to quantify how, thermodynamically, decoherence and the spread of information lead to emergent phenomena: classical objectivity and the flow of time.” To grow North America’s quantum-thermodynamics community, we’ll run annual symposia and an international conference. Our visitors’ program will create the atmosphere of a local watering hole. Outreach will include more posts on this blog—including by guest authors—a quantum-steampunk short-story contest (expect details this fall), and more.

Come visit us by dirigible, train, or gyropter. Air your most thought-provoking quantum-thermodynamics discoveries in a seminar with us, and solicit feedback. Find collaborators, and learn about the latest. The factory wheels are beginning to turn.

With thanks to the John Templeton Foundation for the grant to establish the hub.

# Rocks that roll

In Terry Pratchett’s fantasy novel Soul Music, rock ’n roll arrives in Ankh-Morpork. Ankh-Morpork resembles the London of yesteryear—teeming with heroes and cutthroats, palaces and squalor—but also houses vampires, golems, wizards, and a sentient suitcase. Against this backdrop, a young harpist stumbles upon a mysterious guitar. He forms a band with a dwarf and with a troll who plays tuned rocks, after which the trio calls its style “Music with Rocks In.” The rest of the story consists of satire, drums, and rocks that roll.

The topic of rolling rocks sounds like it should elicit more yawns than an Elvis concert elicited screams. But rocks’ rolling helped recent University of Maryland physics PhD student Zackery Benson win a National Research Council Fellowship. He and his advisor, Wolfgang Losert, converted me into a fan of granular flow.

What I’ve been studying recently. Kind of.

Grains make up materials throughout the galaxy, such as the substance of avalanches. Many granular materials undergo repeated forcing by their environments. For instance, the grains that form an asteroid suffer bombardment from particles flying through outer space. The gravel beneath train tracks is compressed whenever a train passes.

Often, a pattern characterizes the forces in a granular system’s environment. For instance, trains in a particular weight class may traverse some patch of gravel, and the trains may arrive with a particular frequency. Some granular systems come to encode information about those patterns in their microscopic configurations and large-scale properties. So granular flow—little rocks that roll—can impact materials science, engineering, geophysics, and thermodynamics.

Granular flow sounds so elementary, you might expect us to have known everything about it since long before the Beatles’ time. But we didn’t even know until recently how to measure rolling in granular flows.

Envision a grain as a tiny sphere, like a globe of the Earth. Scientists focused mostly on how far grains are translated through space in a flow, analogouslly to how far a globe travels across a desktop if flicked. Recently, scientists measured how far a grain rotates about one axis, like a globe fixed in a frame. Sans frame, though, a globe can spin about more than one axis—about three independent axes. Zack performed the first measurement of all the rotations and translations of all the particles in a granular flow.

Each grain was an acrylic bead about as wide as my pinky nail. Two holes were drilled into each bead, forming an X, for reasons I’ll explain.

Image credit: Benson et al., Phys. Rev. Lett. 129, 048001 (2022).

Zack dumped over 10,000 beads into a rectangular container. Then, he poured in a fluid that filled the spaces between the grains. Placing a weight atop the grains, he exerted a constant pressure on them. Zack would push one of the container’s walls inward, compressing the grains similarly to how a train compresses gravel. Then, he’d decompress the beads. He repeated this compression cycle many times.

Image credit: Benson et al., Phys. Rev. E 103, 062906 (2021).

Each cycle consisted of many steps: Zack would compress the beads a tiny amount, pause, snap pictures, and then compress a tiny amount more. During each pause, the camera activated a fluorescent dye in the fluid, which looked clear in the photographs. Lacking the fluorescent dye, the beads showed up as dark patches. Clear X’s cut through the dark patches, as dye filled the cavities drilled into the beads. From the X’s, Zack inferred every grain’s orientation. He inferred how every grain rotated by comparing the orientation in one snapshot with the orientation in the next snapshot.

Image credit: Benson et al., Phys. Rev. Lett. 129, 048001 (2022).

Wolfgang’s lab had been trying for fifteen years to measure all the motions in a granular flow. The feat required experimental and computational skill. I appreciated the chance to play a minor role, in analyzing the data. Physical Review Letters published our paper last month.

From Zack’s measurements, we learned about the unique roles played by rotations in granular flow. For instance, rotations dominate the motion in a granular system’s bulk, far from the container’s walls. Importantly, the bulk dissipates the most energy. Also, whereas translations are reversible—however far grains shift while compressed, they tend to shift oppositely while decompressed—rotations are not. Such irreversibility can contribute to materials’ aging.

In Soul Music, the spirit of rock ’n roll—conceived of as a force in its own right—offers the guitarist the opportunity to never age. He can live fast, die young, and enjoy immortality as a legend, for his guitar comes from a dusty little shop not entirely of Ankh-Morpork’s world. Such shops deal in fate and fortune, the author maintains. Doing so, he takes a dig at the River Ankh, which flows through the city of Ankh-Morpork. The Ankh’s waters hold so much garbage, excrement, midnight victims, and other muck that they scarcely count as waters:

And there was even an Ankh-Morpork legend, wasn’t there, about some old drum [ . . . ] that was supposed to bang itself if an enemy fleet was seen sailing up the Ankh? The legend had died out in recent centuries, partly because this was the Age of Reason and also because no enemy fleet could sail up the Ankh without a gang of men with shovels going in front.

Such a drum would qualify as magic easily, but don’t underestimate the sludge. As a granular-flow system, it’s more incredible than you might expect.

# These are a few of my favorite steampunk books

As a physicist, one grows used to answering audience questions at the end of a talk one presents. As a quantum physicist, one grows used to answering questions about futuristic technologies. As a quantum-steampunk physicist, one grows used to the question “Which are your favorite steampunk books?”

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?

# One equation to rule them all?

In lieu of composing a blog post this month, I’m publishing an article in Quanta Magazine. The article provides an introduction to fluctuation relations, souped-up variations on the second law of thermodynamics, which helps us understand why time flows in only one direction. The earliest fluctuation relations described classical systems, such as single strands of DNA. Many quantum versions have been proved since. Their proliferation contrasts with the stereotype of physicists as obsessed with unification—with slimming down a cadre of equations into one über-equation. Will one quantum fluctuation relation emerge to rule them all? Maybe, and maybe not. Maybe the multiplicity of quantum fluctuation relations reflects the richness of quantum thermodynamics.

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.

# The power of being able to say “I can explain that”

Caltech condensed-matter theorist Gil Refael explained his scientific raison dê’tre early in my grad-school career: “What really gets me going is seeing a plot [of experimental data] and being able to say, ‘I can explain that.’” The quote has stuck with me almost word for word. When I heard it, I was working deep in abstract quantum information theory and thermodynamics, proving theorems about thought experiments. Embedding myself in pure ideas has always held an aura of romance for me, so I nodded along without seconding Gil’s view.

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 $x$-, $y$-, and $z$-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.

1Experts: The wider world effectively has an infinite temperature because (i) the dominant decoherence is dephasing relative to the $\sigma_z$ 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 $\sigma_x$, $\sigma_y$, and $\sigma_z$ eigenbases.