Project Ant-Man

The craziest challenge I’ve undertaken hasn’t been skydiving; sailing the Amazon on a homemade raft; scaling Mt. Everest; or digging for artifacts atop a hill in a Middle Eastern desert, near midday, during high summer.1 The craziest challenge has been to study the possibility that quantum phenomena affect cognition significantly. 

Most physicists agree that quantum phenomena probably don’t affect cognition significantly. Cognition occurs in biological systems, which have high temperatures, many particles, and watery components. Such conditions quash entanglement (a relationship that quantum particles can share and that can produce correlations stronger than any produceable by classical particles). 

Yet Matthew Fisher, a condensed-matter physicist, proposed a mechanism by which entanglement might enhance coordinated neuron firing. Phosphorus nuclei have spins (quantum properties similar to angular momentum) that might store quantum information for long times when in Posner molecules. These molecules may protect the information from decoherence (leaking quantum information to the environment), via mechanisms that Fisher described.

I can’t check how correct Fisher’s proposal is; I’m not a biochemist. But I’m a quantum information theorist. So I can identify how Posners could process quantum information if Fisher were correct. I undertook this task with my colleague Elizabeth Crosson, during my PhD

Experimentalists have begun testing elements of Fisher’s proposal. What if, years down the road, they find that Posners exist in biofluids and protect quantum information for long times? We’ll need to test whether Posners can share entanglement. But detecting entanglement tends to require control finer than you can exert with a stirring rod. How could you check whether a beakerful of particles contains entanglement?

I asked that question of Adam Bene Watts, a PhD student at MIT, and John Wright, then an MIT postdoc and now an assistant professor in Texas. John gave our project its codename. At a meeting one day, he reported that he’d watched the film Avengers: Endgame. Had I seen it? he asked.

No, I replied. The only superhero movie I’d seen recently had been Ant-Man and the Wasp—and that because, according to the film’s scientific advisor, the movie riffed on research of mine. 

Go on, said John.

Spiros Michalakis, the Caltech mathematician in charge of this blog, served as the advisor. The film came out during my PhD; during a meeting of our research group, Spiros advised me to watch the movie. There was something in it “for you,” he said. “And you,” he added, turning to Elizabeth. I obeyed, to hear Laurence Fishburne’s character tell Ant-Man that another character had entangled with the Posner molecules in Ant-Man’s brain.2 

John insisted on calling our research Project Ant-Man.

John and Adam study Bell tests. Bell test sounds like a means of checking whether the collar worn by your cat still jingles. But the test owes its name to John Stewart Bell, a Northern Irish physicist who wrote a groundbreaking paper in 1964

Say you’d like to check whether two particles share entanglement. You can run an experiment, described by Bell, on them. The experiment ends with a measurement of the particles. You repeat this experiment in many trials, using identical copies of the particles in subsequent trials. You accumulate many measurement outcomes, whose statistics you calculate. You plug those statistics into a formula concocted by Bell. If the result exceeds some number that Bell calculated, the particles shared entanglement.

We needed a variation on Bell’s test. In our experiment, every trial would involve hordes of particles. The experimentalists—large, clumsy, classical beings that they are—couldn’t measure the particles individually. The experimentalists could record only aggregate properties, such as the intensity of the phosphorescence emitted by a test tube.

Adam, MIT physicist Aram Harrow, and I concocted such a Bell test, with help from John. Physical Review A published our paper this month—as a Letter and an Editor’s Suggestion, I’m delighted to report.

For experts: The trick was to make the Bell correlation function nonlinear in the state. We assumed that the particles shared mostly pairwise correlations, though our Bell inequality can accommodate small aberrations. Alas, no one can guarantee that particles share only mostly pairwise correlations. Violating our Bell inequality therefore doesn’t rule out hidden-variables theories. Under reasonable assumptions, though, a not-completely-paranoid experimentalist can check for entanglement using our test. 

One can run our macroscopic Bell test on photons, using present-day technology. But we’re more eager to use the test to characterize lesser-known entities. For instance, we sketched an application to Posner molecules. Detecting entanglement in chemical systems will require more thought, as well as many headaches for experimentalists. But our paper broaches the cask—which I hope to see flow in the next Ant-Man film. Due to debut in 2022, the movie has the subtitle Quantumania. Sounds almost as crazy as studying the possibility that quantum phenomena affect cognition.

1Of those options, I’ve undertaken only the last.

2In case of any confusion: We don’t know that anyone’s brain contains Posner molecules. The movie features speculative fiction.

Random walks

A college professor of mine proposed a restaurant venture to our class. He taught statistical mechanics, the physics of many-particle systems. Examples range from airplane fuel to ice cubes to primordial soup. Such systems contain 1024 particles each—so many particles that we couldn’t track them all if we tried. We can gather only a little information about the particles, so their actions look random.

So does a drunkard’s walk. Imagine a college student who (outside of the pandemic) has stayed out an hour too late and accepted one too many red plastic cups. He’s arrived halfway down a sidewalk, where he’s clutching a lamppost, en route home. Each step has a 50% chance of carrying him leftward and a 50% chance of carrying him rightward. This scenario repeats itself every Friday. On average, five minutes after arriving at the lamppost, he’s back at the lamppost. But, if we wait for a time T, we have a decent chance of finding him a distance \sqrt{T} away. These characteristic typify a simple random walk.

Random walks crop up across statistical physics. For instance, consider a grain of pollen dropped onto a thin film of water. The water molecules buffet the grain, which random-walks across the film. Robert Brown observed this walk in 1827, so we call it Brownian motion. Or consider a magnet at room temperature. The magnet’s constituents don’t walk across the surface, but they orient themselves according random-walk mathematics. And, in quantum many-particle systems, information can spread via a random walk. 

So, my statistical-mechanics professor said, someone should open a restaurant near MIT. Serve lo mein and Peking duck, and call the restaurant the Random Wok.

This is the professor who, years later, confronted another alumna and me at a snack buffet.

“You know what this is?” he asked, waving a pastry in front of us. We stared for a moment, concluded that the obvious answer wouldn’t suffice, and shook our heads.

“A brownie in motion!”

Not only pollen grains undergo Brownian motion, and not only drunkards undergo random walks. Many people random-walk to their careers, trying out and discarding alternatives en route. We may think that we know our destination, but we collide with a water molecule and change course.

Such is the thrust of Random Walks, a podcast to which I contributed an interview last month. Abhigyan Ray, an undergraduate in Mumbai, created the podcast. Courses, he thought, acquaint us only with the successes in science. Stereotypes cast scientists as lone geniuses working in closed offices and silent labs. He resolved to spotlight the collaborations, the wrong turns, the lessons learned the hard way—the random walks—of science. Interviewees range from a Microsoft researcher to a Harvard computer scientist to a neurobiology professor to a genomicist.

You can find my episode on Instagram, Apple Podcasts, Google Podcasts, and Spotify. We discuss the bridging of disciplines; the usefulness of a liberal-arts education in physics; Quantum Frontiers; and the delights of poking fun at my PhD advisor, fellow blogger and Institute for Quantum Information and Matter director John Preskill

The Grand Tour of quantum thermodynamics

Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge. They’d studied classical history, language, and literature; and now, they’d experience what they’d read. Tourists flocked to Rome, Venice, and Florence, as well as to Paris; optional additions included Naples, Switzerland, Germany, and the Netherlands.

Tutors accompanied the tourists, guiding their charges across Europe. The tutors rounded out the young men’s education, instructing them in art, music, architecture, and continental society. I felt like those tutors, this month and last.1

I’m the one in the awkward-looking pose on the left.

I was lecturing in a quantum-thermodynamics mini course, with fellow postdoctoral scholar Matteo Lostaglio. Gabriel Landi, a professor of theoretical physics at the University of São Paolo in Brazil, organized the course. It targeted early-stage graduate students, who’d mastered the core of physics and who wished to immerse in quantum thermodynamics. But the enrollment ranged from PhD and Masters students to undergraduates, postdocs, faculty members, and industry employees.

The course toured quantum thermodynamics similarly to how young noblemen toured Europe. I imagine quantum thermodynamics as a landscape—one inked on a parchment map, with blue whorls representing the sea and with a dragon breathing fire in one corner. Quantum thermodynamics encompasses many communities whose perspectives differ and who wield different mathematical and conceptual tools. These communities translate into city-states, principalities, republics, and other settlements on the map. The class couldn’t visit every city, just as Grand Tourists couldn’t. But tourists had a leg up on us in their time budgets: A Grand Tour lasted months or years, whereas we presented nine hour-and-a-half lectures.

Attendees in Stuttgart

Grand Tourists returned home with trinkets, books, paintings, and ancient artifacts. I like to imagine that the tutors, too, acquired souvenirs. Here are four of my favorite takeaways from the course:

1) Most captivating subfield that I waded into for the course: Thermodynamic uncertainty relations. Researchers have derived these inequalities using nonequilibrium statistical mechanics, a field that encompasses molecular motors, nanorobots, and single strands of DNA. Despite the name “uncertainty relations,” classical and quantum systems obey these inequalities.

Imagine a small system interacting with big systems that have different temperatures and different concentrations of particles. Energy and particles hop between the systems, dissipating entropy (\Sigma) and forming currents. The currents change in time, due to the probabilistic nature of statistical mechanics. 

How much does a current vary, relative to its average value, \langle J \rangle? We quantify this variation with the relative variance, {\rm var}(J) / \langle J \rangle^2. Say that you want a low-variance, predictable current. You’ll have to pay a high entropy cost: \frac{ {\rm var} (J) }{\langle J \rangle^2 } \geq  \frac{2 k_{\rm B} }{\Sigma}, wherein k_{\rm B} denotes Boltzmann’s constant. 

Thermodynamic uncertainty relations govern systems arbitrarily far from equilibrium. We know loads about systems at equilibrium, in which large-scale properties remain approximately constant and no net flows (such as flows of particles) enter or leave the system. We know much about systems close to equilibrium. The regime arbitrarily far from equilibrium is the Wild, Wild West of statistical mechanics. Proving anything about this regime tends to require assumptions and specific models, to say nothing of buckets of work. But thermodynamic uncertainty relations are general, governing classical and quantum systems from molecular motors to quantum dots.

Multiple cats attended our mini course, according to the selfies we received.

2) Most unexpected question: During lecture one, I suggested readings that introduce quantum thermodynamics. The suggestions included two reviews and the article I wrote for Scientific American about quantum steampunk, my angle on quantum thermodynamics. The next day, a participant requested recommendations of steampunk novels. I’d prepared more for requests for justifications of the steps in my derivations. But I forwarded a suggestion given to me twice: The Difference Engine, by William Gibson and Bruce Sterling.

3) Most insightful observation: My fellow tutor—I mean lecturer—pointed out how quantum thermodynamics doesn’t and does diverge from classical thermodynamics. Quantum systems can’t break the second law of thermodynamics, as classical systems can’t. Quantum engines can’t operate more efficiently than Carnot’s engine. Erasing information costs work, regardless of whether the information-bearing degree of freedom is classical or quantum. So broad results about quantum thermodynamics coincide with broad results about classical thermodynamics. We can find discrepancies by focusing on specific physical systems, such as a spring that can be classical or quantum.  

4) Most staggering numbers: Unlike undertaking a Grand Tour, participating in the mini course cost nothing. We invited everyone across the world to join, and 420 participants from 48 countries enrolled. I learned of the final enrollment days before the course began, scrolling through the spreadsheet of participants. Motivated as I had been to double-check my lecture notes, the number spurred my determination like steel on a horse’s flanks.

The Grand Tour gave rise to travelogues and guidebooks read by tourists across the centuries: Mark Twain has entertained readers—partially at his own expense—since 1869 in the memoir The Innocents Abroad. British characters in the 1908 novel A Room with a View diverge in their views of Baedeker’s Handbook to Northern Italy. Our course material, and videos of the lectures, remain online and available to everyone for free. You’re welcome to pack your trunk, fetch your cloak, and join the trip.

A screenshot from the final lecture

1In addition to guiding their wards, tutors kept the young men out of trouble—and one can only imagine what trouble wealthy young men indulged in the year after college. I didn’t share that responsibility.

Seven reasons why I chose to do science in the government

When I was in college, people asked me what I wanted to do with my life. I’d answer, “I want to be of use and to learn always.” The question resurfaced in grad school and at the beginning of my postdoc. I answered that I wanted to do extraordinary science that I’d steer. Academia attracted me most, but I wouldn’t discount alternatives.

Last spring, I accepted an offer to build my research group as a member of NIST, the National Institute for Standards and Technology in the U.S. government. My group will be headquartered on the University of Maryland campus, nestled amongst quantum and interdisciplinary institutes. I’m grateful to be joining NIST, and I’m surprised. I never envisioned myself working for the government. I could have accepted an assistant professorship (and I was extremely grateful for the offers), but NIST swept me off my feet. Here are seven reasons why, for other early-career researchers contemplating possibilities.

1) The science. One event illustrates this reason: The notice of my job offer came from NIST Maryland’s friendly neighborhood Nobel laureate. NIST and the university invested in quantum science years before everyone and her uncle began scrambling to create a quantum institute. That investment has flowered, including in reason (2).

2) The research environment. I wouldn’t say that I have a love affair with the University of Maryland. But I’ve found myself visiting every few years (sometimes blogging about the experience). Why? Much of the quantum community passes through Maryland. Seminars fill the week, visitors fill many offices, and conferences happen once or twice a year. Theorists and experimentalists mingle over lunch and collaborate. 

The university shares two quantum institutes with NIST: QuICS (the Joint Center for Quantum Information and Computer Science) and the JQI (the Joint Quantum Institute). My group will be based at the former and affiliated with the latter. We’ll also belong to IPST (the university’s Institute for Physical Science and Technology), a hub for interdisciplinarity and thermodynamics. When visiting a university, I ask how much researchers collaborate across department lines. I usually hear an answer along the lines of “We value interdisciplinarity, and we wish that we had more of it, but we don’t have much.” Few universities ingrain interdisciplinarity into their bones by dedicating institutes to it.

Maryland’s quantum community and thermodynamics communities bustle and produce. They grant NIST researchers an academic environment, independence to shape their research paths, and the freedom to participate in the broader scientific community. If weary of the three institutes mentioned above, one can explore the university’s Quantum Technology Center and Condensed-Matter-Theory Center

3) The people. The first Maryland quantum researcher I met was the friendly neighborhood Nobel laureate, Bill Phillips. Bill was presenting a keynote address at Dartmouth College’s physics department, where I’d earned my Bachelors. Bill said that he’d attended a small liberal-arts college before pursuing his PhD at MIT. During the question-and-answer session, I welcomed him back to a small liberal-arts college. How, I asked, had he benefited from the liberal arts? Juniata College, Bill said, had made him a good person. MIT had helped make him a good scientist. Since then, I’ve kept in occasional contact with Bill, we’ve attended talks of each other’s, and I’ve watched him exhibit the most curiosity I’ve seen in almost anyone. What more could one wish for in a colleague?

An equality used across thermodynamics bears Chris Jarzynski’s last name, but he never calls the equality what everyone else does. I benefited from Chris’s mentorship during my PhD, despite our working on opposite sides of the country. His awards include not only membership in the National Academy of Sciences, but also an Outstanding Referee designation, for reviewing so many journal submissions in service to the scientific community. Chris calls IPST, the university’s interdisciplinary and thermodynamic institute, his intellectual home. That recommendation suffices for me.

I’ve looked up to Alexey Gorshkov since beginning my PhD. I keep an eye out for Mohammad Hafezi’s and Pratyush Tiwari’s papers. A quantum researcher couldn’t ignore Chris Monroe’s papers if she tried. Postdoctoral and graduate fellowships stock the community with energetic young researchers. Three energetic researchers are joining QuICS as senior Fellows around the time I am. I’ll spare you the rest of my sources of inspiration.

4) The teaching. Most faculty members at R1 research universities teach two to three courses per year. NIST members can teach once every other year. I value teaching and appreciate how teaching benefits not only students, but also instructors. I respect teachers and remain grateful for their influence. I’m grateful to have received reports that I teach well. Because I’ve acquired some skill at communicating, people tend to assume that I adore teaching. I adore presenting talks, but I don’t feel a calling to teach. Mentors have exhorted me to pursue what excites me most and what only I can accomplish. I feel called to do research and to mentor younger researchers. 

Furthermore, if I had to teach much, I wouldn’t have time for writing anything other than papers or grants, such as blog posts. Some of you readers have astonished me with accounts of what my writing means to you. You’ve approached me at conferences, buttonholed me after seminars, and emailed. I’m grateful (as I keep saying, but I mean what I say) for the opportunity to touch lives across the world. I hope to inspire students to take quantum, information-theory, and thermodynamics courses (including the quantum-thermodynamics course that I’d like to teach occasionally). Instructors teach quantum courses throughout the world. No one else writes about Egyptian sarcophagi and the second law of thermodynamics, to my knowledge, or the Russian writer Alexander Pushkin and reproductive science. Perhaps no one should. But, since no one else does, I have to.1

5) The funding. Faculty members complain that they do little apart from applying for grants. Grants fund students, postdocs, travel, summer salaries, equipment, visitors, and workshops. NIST provides primary investigators with research funding every year. Not all the funding that some groups need, but enough to free up time to undertake the research that primary investigators love.

6) The lack of tenure stress. Many junior faculty members fear that they won’t achieve tenure. The fear pushes them away from taking risks in their research programs. This month, I embarked upon a risk that I know I should take but that, had I been facing an assistant professorship, would have given me pause.

7) The acronyms. Above, I introduced NIST (the National Institute of Standards and Technology), UMD (the University of Maryland), QuICS (the Joint Center for Quantum Information and Computer Science), the JQI (the Joint Quantum Institute), and IPST (the Institute for Physical Science and Technology). I’ll also have an affiliation with UMIACS (the University of Maryland Institute for Advanced Computer Science). Where else can one acquire six acronyms? I adore collecting affiliations, which force me to cross intellectual borders. I also enjoy the opportunity to laugh at my CV.

I’ve deferred joining NIST until summer 2021, to complete my postdoctoral fellowship at the Harvard-Smithsonian Institute for Theoretical Atomic, Molecular, and Optical Physics (an organization that needs its acronym, ITAMP, as much as “the Joint Center for Quantum Information and Computer Science” does). After then, please stop by. If you’d like to join my group, please email: I’m accepting applications for PhD and postdoctoral positions this fall. See you in Maryland next year.

1Also, blogging benefits my research. I’ll leave the explanation for another post.

I credit my husband with the Nesquick-NIST/QuICS parallel.

If the (quantum-metrology) key fits…

My maternal grandfather gave me an antique key when I was in middle school. I loved the workmanship: The handle consisted of intertwined loops. I loved the key’s gold color and how the key weighed on my palm. Even more, I loved the thought that the key opened something. I accompanied my mother to antique shops, where I tried unlocking chests, boxes, and drawers.


My grandfather’s antique key

I found myself holding another such key, metaphorically, during the autumn of 2018. MIT’s string theorists had requested a seminar, so I presented about quasiprobabilities. Quasiprobabilities represent quantum states similarly to how probabilities represent a swarm of classical particles. Consider the steam rising from asphalt on a summer day. Calculating every steam particle’s position and momentum would require too much computation for you or me to perform. But we can predict the probability that, if we measure every particle’s position and momentum, we’ll obtain such-and-such outcomes. Probabilities are real numbers between zero and one. Quasiprobabilities can assume negative and nonreal values. We call these values “nonclassical,” because they’re verboten to the probabilities that describe classical systems, such as steam. I’d defined a quasiprobability, with collaborators, to describe quantum chaos. 


David Arvidsson-Shukur was sitting in the audience. David is a postdoctoral fellow at the University of Cambridge and a visiting scholar in the other Cambridge (at MIT). He has a Swedish-and-southern-English accent that I’ve heard only once before and, I learned over the next two years, an academic intensity matched by his kindliness.1 Also, David has a name even longer than mine: David Roland Miran Arvidsson-Shukur. We didn’t know then, but we were destined to journey together, as postdoctoral knights-errant, on a quest for quantum truth.

David studies the foundations of quantum theory: What distinguishes quantum theory from classical? David suspected that a variation on my quasiprobability could unlock a problem in metrology, the study of measurements.


Suppose that you’ve built a quantum computer. It consists of gates—uses of, e.g., magnets or lasers to implement logical operations. A classical gate implements operations such as “add 11.” A quantum gate can implement an operation that involves some number \theta more general than 11. You can try to build your gate correctly, but it might effect the wrong \theta value. You need to measure \theta.

How? You prepare some quantum state | \psi \rangle and operate on it with the gate. \theta imprints itself on the state, which becomes | \psi (\theta) \rangle. Measure some observable \hat{O}. You repeat this protocol in each of many trials. The measurement yields different outcomes in different trials, according to quantum theory. The average amount of information that you learn about \theta per trial is called the Fisher information.


Let’s change this protocol. After operating with the gate, measure another observable, \hat{F}, and postselect: If the \hat{F} measurement yields a desirable outcome f, measure \hat{O}. If the \hat{F}-measurement doesn’t yield the desirable outcome, abort the trial, and begin again. If you choose \hat{F} and f adroitly, you’ll measure \hat{O} only when the trial will provide oodles of information about \theta. You’ll save yourself many \hat{O} measurements that would have benefited you little.2


Why does postselection help us? We could understand easily if the system were classical: The postselection would effectively improve the input state. To illustrate, let’s suppose that (i) a magnetic field implemented the gate and (ii) the input were metal or rubber. The magnetic field wouldn’t affect the rubber; measuring \hat{O} in rubber trials would provide no information about the field. So you could spare yourself \hat{O} measurements by postselecting on the system’s consisting of metal.


Postselection on a quantum system can defy this explanation. Consider optimizing your input state | \psi \rangle, beginning each trial with the quantum equivalent of metal. Postselection could still increase the average amount of information information provided about \theta per trial. Postselection can enhance quantum metrology even when postselection can’t enhance the classical analogue.

David suspected that he could prove this result, using, as a mathematical tool, the quasiprobability that collaborators and I had defined. We fulfilled his prediction, with Hugo Lepage, Aleks Lasek, Seth Lloyd, and Crispin Barnes. Nature Communications published our paper last month. The work bridges the foundations of quantum theory with quantum metrology and quantum information theory—and, through that quasiprobability, string theory. David’s and my quantum quest continues, so keep an eye out for more theory from us, as well as a photonic experiment based on our first paper.


I still have my grandfather’s antique key. I never found a drawer, chest, or box that it opened. But I don’t mind. I have other mysteries to help unlock.


1The morning after my wedding this June, my husband and I found a bouquet ordered by David on our doorstep.

2Postselection has a catch: The \hat{F} measurement has a tiny probability of yielding the desirable outcome. But, sometimes, measuring \hat{O} costs more than preparing | \psi \rangle, performing the gate, and postselecting. For example, suppose that the system is a photon. A photodetector will measure \hat{O}. Some photodetectors have a dead time: After firing, they take a while to reset, to be able to fire again. The dead time can outweigh the cost of the beginning of the experiment.

A quantum walk down memory lane

In elementary and middle school, I felt an affinity for the class three years above mine. Five of my peers had siblings in that year. I carpooled with a student in that class, which partnered with mine in holiday activities and Grandparents’ Day revues. Two students in that class stood out. They won academic-achievement awards, represented our school in science fairs and speech competitions, and enrolled in rigorous high-school programs.

Those students came to mind as I grew to know David Limmer. David is an assistant professor of chemistry at the University of California, Berkeley. He studies statistical mechanics far from equilibrium, using information theory. Though a theorist ardent about mathematics, he partners with experimentalists. He can pass as a physicist and keeps an eye on topics as far afield as black holes. According to his faculty page, I discovered while writing this article, he’s even three years older than I. 

I met David in the final year of my PhD. I was looking ahead to postdocking, as his postdoc fellowship was fading into memory. The more we talked, the more I thought, I’d like to be like him.


I had the good fortune to collaborate with David on a paper published by Physical Review A this spring (as an Editors’ Suggestion!). The project has featured in Quantum Frontiers as the inspiration for a rewriting of “I’m a little teapot.” 

We studied a molecule prevalent across nature and technologies. Such molecules feature in your eyes, solar-fuel-storage devices, and more. The molecule has two clumps of atoms. One clump may rotate relative to the other if the molecule absorbs light. The rotation switches the molecule from a “closed” configuration to an “open” configuration.

Molecular switch

These molecular switches are small, quantum, and far from equilibrium; so modeling them is difficult. Making assumptions offers traction, but many of the assumptions disagreed with David. He wanted general, thermodynamic-style bounds on the probability that one of these molecular switches would switch. Then, he ran into me.

I traffic in mathematical models, developed in quantum information theory, called resource theories. We use resource theories to calculate which states can transform into which in thermodynamics, as a dime can transform into ten pennies at a bank. David and I modeled his molecule in a resource theory, then bounded the molecule’s probability of switching from “closed” to “open.” I accidentally composed a theme song for the molecule; you can sing along with this post.

That post didn’t mention what David and I discovered about quantum clocks. But what better backdrop for a mental trip to elementary school or to three years into the future?

I’ve blogged about autonomous quantum clocks (and ancient Assyria) before. Autonomous quantum clocks differ from quantum clocks of another type—the most precise clocks in the world. Scientists operate the latter clocks with lasers; autonomous quantum clocks need no operators. Autonomy benefits you if you want for a machine, such as a computer or a drone, to operate independently. An autonomous clock in the machine ensures that, say, the computer applies the right logical gate at the right time.

What’s an autonomous quantum clock? First, what’s a clock? A clock has a degree of freedom (e.g., a pair of hands) that represents the time and that moves steadily. When the clock’s hands point to 12 PM, you’re preparing lunch; when the clock’s hands point to 6 PM, you’re reading Quantum Frontiers. An autonomous quantum clock has a degree of freedom that represents the time fairly accurately and moves fairly steadily. (The quantum uncertainty principle prevents a perfect quantum clock from existing.)

Suppose that the autonomous quantum clock constitutes one part of a machine, such as a quantum computer, that the clock guides. When the clock is in one quantum state, the rest of the machine undergoes one operation, such as one quantum logical gate. (Experts: The rest of the machine evolves under one Hamiltonian.) When the clock is in another state, the rest of the machine undergoes another operation (evolves under another Hamiltonian).

Clock 2

Physicists have been modeling quantum clocks using the resource theory with which David and I modeled our molecule. The math with which we represented our molecule, I realized, coincided with the math that represents an autonomous quantum clock.

Think of the molecular switch as a machine that operates (mostly) independently and that contains an autonomous quantum clock. The rotating clump of atoms constitutes the clock hand. As a hand rotates down a clock face, so do the nuclei rotate downward. The hand effectively points to 12 PM when the switch occupies its “closed” position. The hand effectively points to 6 PM when the switch occupies its “open” position.

The nuclei account for most of the molecule’s weight; electrons account for little. They flit about the landscape shaped by the atomic clumps’ positions. The landscape governs the electrons’ behavior. So the electrons form the rest of the quantum machine controlled by the nuclear clock.

Clock 1

Experimentalists can create and manipulate these molecular switches easily. For instance, experimentalists can set the atomic clump moving—can “wind up” the clock—with ultrafast lasers. In contrast, the only other autonomous quantum clocks that I’d read about live in theory land. Can these molecules bridge theory to experiment? Reach out if you have ideas!

And check out David’s theory lab on Berkeley’s website and on Twitter. We all need older siblings to look up to.

What can you do in 48 hours?

Have you ever wondered what can be done in 48 hours? For instance, our heart beats around 200 000 times. One of the biggest supercomputers crunches petabytes (peta = 1015) of numbers to simulate an experiment that took Google’s quantum processor only 300 seconds to run. In 48 hours, one can also participate in the Sciathon with almost 500 young researchers from more than 80 countries! 

Two weeks ago I participated in a scientific marathon, the Sciathon. The structure of this event roughly resembled a hackathon. I am sure many readers are familiar with the idea of a hackathon from personal experience. For those unfamiliar — a hackathon is an intense collaborative event, usually organized over the weekend, during which people with different backgrounds work in groups to create prototypes of functioning software or hardware. For me, it was the very first time to have firsthand experience with a hackathon-like event!

The Sciathon was organized by the Lindau Nobel Laureate Meetings (more about the meetings with Nobel laureates, which happen annually in the lovely German town of Lindau, in another blogpost, I promise!) This year, unfortunately, the face-to-face meeting in Lindau was postponed until the summer of 2021. Instead, the Lindau Nobel Laureate Meetings alumni and this year’s would-be attendees had an opportunity to gather for the Sciathon, as well as the Online Science Days earlier this week, during which the best Sciathon projects were presented.

The participants of the Sciathon could choose to contribute new views, perspectives and solutions to three main topics: Lindau Guidelines, Communicating Climate Change and Capitalism After Corona. The first topic concerned an open, cooperative science community where data and knowledge are freely shared, the second — how scientists could show that the climate crisis is just as big a threat as the SARS-CoV-19 virus, and the last — how to remodel our current economic systems so that they are more robust to unexpected sudden crises. More detailed descriptions of each topic can be found on the official Sciathon webpage.

My group of ten eager scientists, mostly physicists, from master students to postdoctoral researchers, focused on the first topic. In particular, our goal was to develop a method of familiarizing high school students with the basics of quantum information and computation. We envisioned creating an online notebook, where an engaging story would be intertwined with interactive blocks of Python code utilizing the open-source quantum computing toolkit Qiskit. This hands-on approach would enable students to play with quantum systems described in the story-line by simply running the pre-programmed commands with a click of the mouse and then observe how “experiment” matches “the theory”. We decided to work with a system comprising one or two qubits and explain such fundamental concepts in quantum physics as superposition, entanglement and measurement. The last missing part was a captivating story.

The story we came up with involved two good friends from the lab, Miss Schrödinger and Miss Pauli, as well as their kittens, Alice and Bob. At first, Alice and Bob seemed to be ordinary cats, however whenever they sipped quantum milk, they would turn into quantum cats, or as quantum physicists would say — kets. Do I have to remind the reader that a quantum cat, unlike an ordinary one, could be both awake and asleep at the same time?

Miss Schrödinger was a proud cat owner who not only loved her cat, but also would take hundreds of pictures of Alice and eagerly upload them on social media. Much to Miss Schrödinger’s surprise, none of the pictures showed Alice partly awake and partly asleep — the ket would always collapse to the cat awake or the cat asleep! Every now and then, Miss Pauli would come to visit Miss Schrödinger and bring her own cat Bob. While the good friends were chit-chatting over a cup of afternoon tea, the cats sipped a bit of quantum milk and started to play with a ball of wool, resulting in a cute mess of two kittens tangled up in wool. Every time after coming back home, Miss Pauli would take a picture of Bob and share it with Miss Schrödinger, who would obviously also take a picture of Alice. After a while, the young scientists started to notice some strange correlations between the states of their cats… 

The adventures of Miss Schrödinger and her cat continue! For those interested, you can watch a short video about our project! 

Overall, I can say that I had a lot of fun participating in the Sciathon. It was an intense yet extremely gratifying event. In addition to the obvious difficulty of racing against the clock, our group also had to struggle with coordinating video calls between group members scattered across three almost equidistant time zones — Eastern Australian, Central European and Central US! During the Sciathon I had a chance to interact with other science enthusiasts from different backgrounds and work on something from outside my area of expertise. I would strongly encourage anyone to participate in hackathon-like events to break the daily routine, particularly monotonous during the lockdown, and unleash one’s creative spirit. Such events can also be viewed as an opportunity to communicate science and scientific progress to the public. Lastly, I would like to thank other members of my team — collaborating with you during the Sciathon was a blast!

During the Sciathon, we had many brainstorming sessions. You can see most of the members of my group in this video call (from left to right, top to bottom): Shuang, myself, Martin, Kyle, Hadewijch, Saskia, Michael and Bartłomiej. The team also included Ahmed and Watcharaphol.

Eleven risks of marrying a quantum information scientist

Some of you may have wondered whether I have a life. I do. He’s a computer scientist, and we got married earlier this month. 

Marrying a quantum information scientist comes with dangers not advertised in any Brides magazine (I assume; I’ve never opened a copy of Brides magazine). Never mind the perils of gathering together Auntie So-and-so and Cousin Such-and-such, who’ve quarreled since you were six; or spending tens of thousands of dollars on one day; or assembling two handfuls of humans during a pandemic. Beware the risks of marrying someone who unconsciously types “entropy” when trying to type “entry,” twice in a row.

1) She’ll introduce you to friends as “a classical computer scientist.” They’d assume, otherwise, that he does quantum computer science. Of course. Wouldn’t you?


2) The quantum punning will commence months before the wedding. One colleague wrote, “Many congratulations! Now you know the true meaning of entanglement.” Quantum particles can share entanglement. If you measure entangled particles, your outcomes can exhibit correlations stronger than any produceable by classical particles. As a card from another colleague read, “May you stay forever entangled, with no decoherence.”

I’d rather not dedicate much of a wedding article to decoherence, but suppose that two particles are maximally entangled (can generate the strongest correlations possible). Suppose that particle 2 heats up or suffers bombardment by other particles. The state of particle 2 decoheres as the entanglement between 1 and 2 frays. Equivalently, particle 2 entangles with its environment, and particle 2 can entangle only so much: The more entanglement 2 shares with the environment, the less entanglement 2 can share with 1. Physicists call entanglement—ba-duh-bummonogamous. 

The matron-of-honor toast featured another entanglement joke, as well as five more physics puns.1 (She isn’t a scientist, but she did her research.) She’ll be on Zoom till Thursday; try the virtual veal.


3) When you ask what sort of engagement ring she’d like, she’ll mention black diamonds. Experimentalists and engineers are building quantum computers from systems of many types, including diamond. Diamond consists of carbon atoms arranged in a lattice. Imagine expelling two neighboring carbon atoms and replacing one with a nitrogen atom. You’ll create a nitrogen-vacancy center whose electrons you can control with light. Such centers color the diamond black but let you process quantum information.

If I’d asked my fiancé for a quantum computer, we’d have had to wait 20 years to marry. He gave me an heirloom stone instead.


4) When a wedding-gown shopkeeper asks which sort of train she’d prefer, she’ll inquire about Maglevs. I dislike shopping, as the best man knows better than most people. In middle school, while our classmates spent their weekends at the mall, we stayed home and read books. But I filled out gown shops’ questionnaires. 

“They want to know what kinds of material I like,” I told the best man over the phone, “and what styles, and what type of train. I had to pick from four types of train. I didn’t even know there were four types of train!”

“Steam?” guessed the best man. “Diesel?”

His suggestions appealed to me as a quantum thermodynamicist. Thermodynamics is the physics of energy, which engines process. Quantum thermodynamicists study how quantum phenomena, such as entanglement, can improve engines. 

“Get the Maglev train,” the best man added. “Low emissions.”

“Ooh,” I said, “that’s superconducting.” Superconductors are quantum systems in which charge can flow forever, without dissipating. Labs at Yale, at IBM, and elsewhere are building quantum computers from superconductors. A superconductor consists of electrons that pair up with help from their positively charged surroundings—Cooper pairs. Separating Cooper-paired electrons requires an enormous amount of energy. What other type of train would better suit a wedding?

I set down my phone more at ease. Later, pandemic-era business closures constrained me to wearing a knee-length dress that I’d worn at graduations. I didn’t mind dodging the train.


5) When you ask what style of wedding dress she’ll wear, she’ll say that she likes her clothing as she likes her equations. Elegant in their simplicity.

6) You’ll plan your wedding for wedding season only because the rest of the year conflicts with more seminars, conferences, and colloquia. The quantum-information-theory conference of the year takes place in January. We wanted to visit Australia in late summer, and Germany in autumn, for conferences. A quantum-thermodynamics conference takes place early in the spring, and the academic year ends in May. Happy is the June bride; happier is the June bride who isn’t preparing a talk.

7) An MIT chaplain will marry you. Who else would sanctify the union of a physicist and a computer scientist?

8) You’ll acquire more in-laws than you bargained for. Biological parents more than suffice for most spouses. My husband has to contend with academic in-laws, as my PhD supervisor is called my “academic father.”


Academic in-laws of my husband’s attending the wedding via Zoom.

9) Your wedding can double as a conference. Had our wedding taken place in person, collaborations would have flourished during the cocktail hour. Papers would have followed; their acknowledgements sections would have nodded at the wedding; and I’d have requested copies of all manuscripts for our records—which might have included our wedding album.

10) You’ll have trouble identifying a honeymoon destination where she won’t be tempted to give a seminar. I thought that my then-fiancé would enjoy Vienna, but it boasts a quantum institute. So do Innsbruck and Delft. A colleague-friend works in Budapest, and I owe Berlin a professional visit. The list grew—or, rather, our options shrank. But he turned out not to mind my giving a seminar. The pandemic then cancelled our trip, so we’ll stay abroad for a week after some postpandemic European conference (hint hint).

11) Your wedding will feature on the blog of Caltech’s Institute for Quantum Information and Matter. Never mind The New York Times. Where else would you expect to find a quantum information physicist? I feel fortunate to have found someone with whom I wouldn’t rather be anywhere else.



1“I know that if Nicole picked him to stand by her side, he must be a FEYNMAN and not a BOZON.”

Up we go! or From abstract theory to experimental proposal

Mr. Mole is trapped indoors, alone. Spring is awakening outside, but he’s confined to his burrow. Birds are twittering, and rabbits are chattering, but he has only himself for company.

Sound familiar? 

Spring—crocuses, daffodils, and hyacinths budding; leaves unfurling; and birds warbling—burst upon Cambridge, Massachusetts last month. The city’s shutdown vied with the season’s vivaciousness. I relieved the tension by rereading The Wind in the Willows, which I’ve read every spring since 2017. 

Project Gutenberg offers free access to Kenneth Grahame’s 1908 novel. He wrote the book for children, but never mind that. Many masterpieces of literature happen to have been written for children.

Book cover

One line in the novel demanded, last year, that I memorize it. On page one, Mole is cleaning his house beneath the Earth’s surface. He’s been dusting and whitewashing for hours when the spring calls to him. Life is pulsating on the ground and in the air above him, and he can’t resist joining the party. Mole throws down his cleaning supplies and tunnels upward through the soil: “he scraped and scratched and scrabbled and scrooged, and then he scrooged again and scrabbled and scratched and scraped.”

The quotation appealed to me not only because of its alliteration and chiasmus. Mole’s journey reminded me of research. 

Take a paper that I published last month with Michael Beverland of Microsoft Research and Amir Kalev of the Joint Center for Quantum Information and Computer Science (now of the Information Sciences Institute at the University of Southern California). We translated a discovery from the abstract, mathematical language of quantum-information-theoretic thermodynamics into an experimental proposal. We had to scrabble, but we kept on scrooging.

Mole 1

Over four years ago, other collaborators and I uncovered a thermodynamics problem, as did two other groups at the same time. Thermodynamicists often consider small systems that interact with large environments, like a magnolia flower releasing its perfume into the air. The two systems—magnolia flower and air—exchange things, such as energy and scent particles. The total amount of energy in the flower and the air remains constant, as does the total number of perfume particles. So we call the energy and the perfume-particle number conserved quantities. 

We represent quantum conserved quantities with matrices Q_1 and Q_2. We nearly always assume that, in this thermodynamic problem, those matrices commute with each other: Q_1 Q_2 = Q_2 Q_1. Almost no one mentions this assumption; we make it without realizing. Eliminating this assumption invalidates a derivation of the state reached by the small system after a long time. But why assume that the matrices commute? Noncommutation typifies quantum physics and underlies quantum error correction and quantum cryptography.

What if the little system exchanges with the large system thermodynamic quantities represented by matrices that don’t commute with each other?


Colleagues and I began answering this question, four years ago. The small system, we argued, thermalizes to near a quantum state that contains noncommuting matrices. We termed that state, e^{ - \sum_\alpha \beta_\alpha Q_\alpha } / Z, the non-Abelian thermal state. The Q_\alpha’s represent conserved quantities, and the \beta_\alpha’s resemble temperatures. The real number Z ensures that, if you measure any property of the state, you’ll obtain some outcome. Our arguments relied on abstract mathematics, resource theories, and more quantum information theory.

Over the past four years, noncommuting conserved quantities have propagated across quantum-information-theoretic thermodynamics.1 Watching the idea take root has been exhilarating, but the quantum information theory didn’t satisfy me. I wanted to see a real physical system thermalize to near the non-Abelian thermal state.

Michael and Amir joined the mission to propose an experiment. We kept nosing toward a solution, then dislodging a rock that would shower dirt on us and block our path. But we scrabbled onward.


Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. These spin components are represented by matrices Q_x = S_x, Q_y = S_y, and Q_z = S_z that don’t commute with each other. 

A couple of qubits can form the small system, analogous to the magnolia flower. The rest of the qubits form the large system, analogous to the air. I constructed a Hamiltonian—a matrix that dictates how the qubits evolve—that transfers quanta of all the spin’s components between the small system and the large. (Experts: The Heisenberg Hamiltonian transfers quanta of all the spin components between two qubits while conserving S_{x, y, z}^{\rm tot}.)

The Hamiltonian led to our first scrape: I constructed an integrable Hamiltonian, by accident. Integrable Hamiltonians can’t thermalize systems. A system thermalizes by losing information about its initial conditions, evolving to a state with an exponential form, such as e^{ - \sum_\alpha \beta_\alpha Q_\alpha } / Z. We clawed at the dirt and uncovered a solution: My Hamiltonian coupled together nearest-neighbor qubits. If the Hamiltonian coupled also next-nearest-neighbor qubits, or if the ions formed a 2D or 3D array, the Hamiltonian would be nonintegrable.


We had to scratch at every stage—while formulating the setup, preparation procedure, evolution, measurement, and prediction. But we managed; Physical Review E published our paper last month. We showed how a quantum system can evolve to the non-Abelian thermal state. Trapped ions, ultracold atoms, and quantum dots can realize our experimental proposal. We imported noncommuting conserved quantities in thermodynamics from quantum information theory to condensed matter and atomic, molecular, and optical physics.

As Grahame wrote, the Mole kept “working busily with his little paws and muttering to himself, ‘Up we go! Up we go!’ till at last, pop! his snout came out into the sunlight and he found himself rolling in the warm grass of a great meadow.”

Mole 2

1See our latest paper’s introduction for references.

On the merits of flatworm reproduction

On my right sat a quantum engineer. She was facing a melanoma specialist who works at a medical school. Leftward of us sat a networks expert, a flatworm enthusiast, and a condensed-matter theorist.

Farther down sat a woman who slices up mouse brains. 

Welcome to “Coherent Spins in Biology,” a conference that took place at the University of California, Los Angeles (UCLA) this past December. Two southern Californians organized the workshop: Clarice Aiello heads UCLA’s Quantum Biology Tech lab. Thorsten Ritz, of the University of California, Irvine, cofounded a branch of quantum biology.

Clarice logo

Quantum biology served as the conference’s backdrop. According to conventional wisdom, quantum phenomena can’t influence biology significantly: Biological systems have high temperatures, many particles, and fluids. Quantum phenomena, such as entanglement (a relationship that quantum particles can share), die quickly under such conditions.

Yet perhaps some survive. Quantum biologists search for biological systems that might use quantum resources. Then, they model and measure the uses and resources. Three settings (at least) have held out promise during the past few decades: avian navigation, photosynthesis, and olfaction. You can read about them in this book, cowritten by a conference participant for the general public. I’ll give you a taste (or a possibly quantum smell?) by sketching the avian-navigation proposal, developed by Thorsten and colleagues.

Bird + flower

Birds migrate southward during the autumn and northward during the spring. How do they know where to fly? At least partially by sensing the Earth’s magnetic field, which leads compass needles to point northward. How do birds sense the field?

Possibly with a protein called “cryptochrome.” A photon (a particle of light) could knock an electron out of part of the protein and into another part. Each part would have one electron that lacked a partner. The electrons would share entanglement. One electron would interact with the Earth’s magnetic field differently than its partner, because its surroundings would differ. (Experts: The electrons would form a radical pair. One electron would neighbor different atoms than the other, so the electron would experience a different local magnetic field. The discrepancy would change the relative phase between the electrons’ spins.) The discrepancy could affect the rate at which the chemical system could undergo certain reactions. Which reactions occur could snowball into large and larger effects, eventually signaling the brain about where the bird should fly.

Angry bird

Quantum mechanics and life rank amongst the universe’s mysteries. How could a young researcher resist the combination? A postdoc warned me away, one lunchtime at the start of my PhD. Quantum biology had enjoyed attention several years earlier, he said, but noise the obscured experimental data. Controversy marred the field.

I ate lunch with that postdoc in 2013. Interest in quantum biology is reviving, as evidenced in the conference. Two reasons suggested themselves: new technologies and new research avenues. For example, Thorsten described the disabling and deletion of genes that code for cryptochrome. Such studies require years’ more work but might illuminate whether cryptochrome affects navigation.

Open door

The keynote speaker, Harvard’s Misha Lukin, illustrated new technologies and new research avenues. Misha’s lab has diamonds that contain quantum defects, which serve as artificial atoms. The defects sense tiny magnetic fields and temperatures. Misha’s group applies these quantum sensors to biology problems.

For example, different cells in an embryo divide at different times. Imagine reversing the order in which the cells divide. Would the reversal harm the organism? You could find out by manipulating the temperatures in different parts of the embryo: Temperature controls the rate at which cells divide.

Misha’s team injected nanoscale diamonds into a worm embryo. (See this paper for a related study.) The diamonds reported the temperature at various points in the worm. This information guided experimentalists who heated the embryo with lasers.

The manipulated embryos grew into fairly normal adults. But their cells, and their descendants’ cells, cycled through the stages of life slowly. This study exemplified, to me, one of the most meaningful opportunities for quantum physicists interested in biology: to develop technologies and analyses that can answer biology questions.


I mentioned, in an earlier blog post, another avenue emerging in quantum biology: Physicist Matthew Fisher proposed a mechanism by which entanglement might enhance coordinated neuron firing. My collaborator Elizabeth Crosson and I analyzed how the molecules in Matthew’s proposal—Posner clusters—could process quantum information. The field of Posner quantum biology had a population of about two, when Elizabeth and I entered, and I wondered whether anyone would join us.

The conference helped resolve my uncertainty. Three speakers (including me) presented work based on Matthew’s; two other participants were tilling the Posner soil; and another speaker mentioned Matthew’s proposal. The other two Posner talks related data from three experiments. The experimentalists haven’t finished their papers, so I won’t share details. But stay tuned.

Posner 2

Posner molecule (image by Swift et al.)

Clarice and Thorsten’s conference reminded me of a conference I’d participated in at the end of my PhD: Last month, I moonlighted as a quantum biologist. In 2017, I moonlighted as a quantum-gravity theorist. Two years earlier, I’d been dreaming about black holes and space-time. At UCLA, I was finishing the first paper I’ve coauthored with biophysicists. What a toolkit quantum information theory and thermodynamics provide, that it can unite such disparate fields. 

The contrast—on top of what I learned at UCLA—filled my mind for weeks. And reminded me of the description of asexual reproduction that we heard from the conference’s flatworm enthusiast. According to Western Michigan University’s Wendy Beane, a flatworm “glues its butt down, pops its head off, and grows a new one. Y’know. As one does.” 

I hope I never flinch from popping my head off and growing a new one—on my quantum-information-thermodynamics spine—whenever new science calls for figuring out.


With thanks to Clarice, Thorsten, and UCLA for their invitation and hospitality.