“A theorist I can actually talk with”

Haunted mansions have ghosts, football teams have mascots, and labs have in-house theorists. I found myself posing as a lab’s theorist at Caltech. The gig began when Oskar Painter, a Caltech experimentalist, emailed that he’d read my first paper about quantum chaos. Would I discuss the paper with the group?

Oskar’s lab was building superconducting qubits, tiny circuits in which charge can flow forever. The lab aimed to control scores of qubits, to develop a quantum many-body system. Entanglement—strong correlations that quantum systems can sustain and everyday systems can’t—would spread throughout the qubits. The system could realize phases of matter—like many-particle quantum chaos—off-limits to most materials.

How could Oskar’s lab characterize the entanglement, the entanglement’s spread, and the phases? Expert readers will suggest measuring an entropy, a gauge of how much information this part of the system holds about that part. But experimentalists have had trouble measuring entropies. Besides, one measurement can’t capture many-body entanglement; such entanglement involves too many intricacies. Oskar was searching for arrows to add to his lab’s measurement quiver.

Mascot

In-house theorist?

I’d proposed a protocol for measuring a characterization of many-body entanglement, quantum chaos, and thermalization—a property called “the out-of-time-ordered correlator.” The protocol appealed to Oskar. But practicalities limit quantum many-body experiments: The more qubits your system contains, the more the system can contact its environment, like stray particles. The stronger the interactions, the more the environment entangles with the qubits, and the less the qubits entangle with each other. Quantum information leaks from the qubits into their surroundings; what happens in Vegas doesn’t stay in Vegas. Would imperfections mar my protocol?

I didn’t know. But I knew someone who could help us find out.

Justin Dressel works at Chapman University as a physics professor. He’s received the highest praise that I’ve heard any experimentalist give a theorist: “He’s a theorist I can actually talk to.” With other collaborators, Justin and I simplified my scheme for measuring out-of-time-ordered correlators. Justin knew what superconducting-qubit experimentalists could achieve, and he’d been helping them reach for more.

How about, I asked Justin, we simulate our protocol on a computer? We’d code up virtual superconducting qubits, program in interactions with the environment, run our measurement scheme, and assess the results’ noisiness. Justin had the tools to simulate the qubits, but he lacked the time. 

Know any postdocs or students who’d take an interest? I asked.

Chapman.001

Chapman University’s former science center. Don’t you wish you spent winters in California?

José Raúl González Alonso has a smile like a welcome sign and a coffee cup glued to one hand. He was moving to Chapman University to work as a Grand Challenges Postdoctoral Fellow. José had built simulations, and he jumped at the chance to study quantum chaos.

José confirmed Oskar’s fear and other simulators’ findings: The environment threatens measurements of the out-of-time-ordered correlator. Suppose that you measure this correlator at each of many instants, you plot the correlator against time, and you see the correlator drop. If you’ve isolated your qubits from their environment, we can expect them to carry many-body entanglement. Golden. But the correlator can drop if, instead, the environment is harassing your qubits. You can misdiagnose leaking as many-body entanglement.

OTOC plots

Our triumvirate identified a solution. Justin and I had discovered another characterization of quantum chaos and many-body entanglement: a quasiprobability, a quantum generalization of a probability.  

The quasiprobability contains more information about the entanglement than the out-of-time-ordered-correlator does. José simulated measurements of the quasiprobability. The quasiprobability, he found, behaves one way when the qubits entangle independently of their environment and behaves another way when the qubits leak. You can measure the quasiprobability to decide whether to trust your out-of-time-ordered-correlator measurement or to isolate your qubits better. The quasiprobability enables us to avoid false positives.

Physical Review Letters published our paper last month. Working with Justin and José deepened my appetite for translating between the abstract and the concrete, for proving abstractions as a theorist’s theorist and realizing them experimentally as a lab’s theorist. Maybe, someday, I’ll earn the tag “a theorist I can actually talk with” from an experimentalist. For now, at least I serve better than a football-team mascot.

Symmetries and quantum error correction

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

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

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

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

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

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

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

Covariant codes for quantum computation

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

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

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

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

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

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

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

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

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

From quantum computation to many-body physics and quantum gravity

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

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

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

AdSCFT-01

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

What’s next?

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

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

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

Why care about physics that doesn’t care about us?

A polar vortex had descended on Chicago.

I was preparing to fly in, scheduled to present a seminar at the University of Chicago. My boyfriend warned, from Massachusetts, that the wind chill effectively lowered the temperature to -50 degrees F. I’d last encountered -50 degrees F in the short story “To Build a Fire,” by Jack London. Spoiler alert: The protagonist fails to build a fire and freezes to death.

The story exemplifies naturalism, according to my 11th-grade English class. The naturalist movement infiltrated American literature and art during the late 19th century. Naturalists portrayed nature as as harsh and indifferent: The winter doesn’t care if Jack London’s protagonist dies.

The protagonist lingered in my mind as my plane took off. I was flying into a polar vortex for physics, the study of nature. Physics doesn’t care about me. How can I care so much about physics? How can humans generally?

Peeling apart that question, I found more layers than I’d packed for protection against the polar vortex.

Tweet

Intellectualism formed the parka of the answer: You can’t hug space, time, information, energy, and the nature of reality. You can’t smile at them and watch them smile back. But their abstractness doesn’t block me from engaging with them; it attracts me. Ideas attract me; their purity does. Physics consists partially of a framework of ideas—of mathematical models, of theorems and examples, of the hypotheses and plots and revisions that underlie a theory.

The framework of physics needs construction. Some people compose songs; some build businesses; others bake soufflés; I used to do arts and crafts. Many humans create—envision, shape, mold, and coordinate—with many different materials. Theoretical physics overflows with materials and with opportunities to create. As humans love to create, we can love physics. Theoretical-physics materials consist of ideas, which might sound less suited to construction than paint does. But painters glob mixtures of water, resin, acrylic, and pigment onto woven fabric. Why shouldn’t ideas appeal as much as resin does? I build worlds in my head for a living. Doesn’t that sound romantic?

Painters derive joy from painting; dancers derive joy from moving; physics offers outlets for many skills. Doing physics, I use math. I learn history: What paradoxes about quantum theory did Albert Einstein pose to Niels Bohr? I write papers and blog posts, and I present seminars and colloquia. I’ve moonlighted as a chemist, studied biology, dipped into computer science, and sought to improve engineering. Beyond these disciplines, physics requires uniquely physical skills: the identification of questions about the natural world, the translation of those questions into math, and the translation of mathematical results into statements about the natural world. In college, I hated having to choose a major because I wanted to study everything. Physics lets me.

Easel

My attraction to physics worried me in college. Jim Yong Kim became Dartmouth’s president in my junior year. Jim, who left to helm the World Bank, specializes in global health. He insisted that “the world’s troubles are your troubles,” quoting former Dartmouth president John Sloan Dickey. I was developing a specialization in quantum information theory. I wasn’t trying to contain ebola, mitigate droughts, or eradicate Alzheimer’s disease. Should I not have been trying to save the world?

I could help save the world, a mentor said, through theoretical physics.1 Society needs a few people to develop art, a few to write music, a few to curate history, and a few to study the nature of the universe. Such outliers help keep us human, and the reinforcement of humanity helps save the world. You may indulge in physics, my mentor said, because physics affords the opportunity to do good. If I appreciate that opportunity, how can I not appreciate physics?

The opportunity to do good has endeared physics to me more as I’ve advanced. The more I advance, the fewer women I see. According to the American Physical Society (APS), in 2017, women received about 21% of the physics Bachelor’s degrees awarded in the U.S. Women received about 18% of the doctorates. In 2010, women numbered 8% of the full professors in U.S. departments that offered Bachelor’s or higher degrees in physics. The APS is conducting studies, coordinating workshops, and offering grants to improve the gender ratio. Departments, teachers, and mentors are helping. They have my gratitude. Yet they can accomplish only so much, especially since many are men. They can encourage women to change the gender ratio; they can’t change the ratio directly. Only women can, and few women are undertaking the task. Physics affords an opportunity to do good—to improve a field’s climate, to mentor, and to combat stereotypes—that few people can tackle. For that opportunity, I’m grateful to physics.

World

Physics lifts us beyond the Platonic realm of ideas in two other ways. At Caltech, I once ate lunch with Charlie Marcus. Marcus is a Microsoft researcher and a professor of physics at the University of Copenhagen’s Niels Bohr Institute. His lab is developing topological quantum computers, in which calculations manifest as braids. Why, I asked, does quantum computing deserve a large chunk of Marcus’s life?

Two reasons, he replied. First, quantum computing straddles the border between foundational physics and applications. Quantum science satisfies the intellect but doesn’t tether us to esoterica. Our science could impact technology, industry and society. Second, the people. Quantum computing has a community steeped in congeniality.

Marcus’s response delighted me: His reasons for caring about quantum computing coincided with two of mine. Reason two has expanded, in my mind, to opportunities for engagement with people. Abstractions attract me partially because intellectualism runs in my family. I grew up surrounded by readers, encouraged to ask questions. Physics enables me to participate in a family tradition and to extend that tradition to the cosmos. My parents now ask me the questions—about black holes and about whether I’m staying warm in Chicago.

Beyond family, physics enables me to engage with you. This blog has connected me to undergraduates, artists, authors, computer programmers, science teachers, and museum directors across the world. Scientific outreach inspires reading, research, art, and the joy of learning. I love those outcomes, participating in them, and engaging with you.

Chain

Why fly into a polar vortex for the study of nature—why care about physics that can’t care about us? In my case, primarily because of the ideas, the abstraction, and the chances to create and learn. Partially for the chance to help save the world through humanness, outreach, and a gender balance. Partially for the chance to impact technology, and partially to connect with people: Physics can strengthen ties to family and can introduce you to individuals across the globe. And physics can— heck, tomorrow is February 14th—lead you to someone who cares enough to track Chicago’s weather from Cambridge.

 

1I’m grateful that Jim Kim, too, encouraged me to pursue theoretical physics.

Humans can intuit quantum physics.

One evening this January, audience members packed into a lecture hall in MIT’s physics building. Undergraduates, members of the public, faculty members, and other scholars came to watch a film premiere and a panel discussion. NOVA had produced the film, “Einstein’s Quantum Riddle,” which stars entanglement. Entanglement is a relationship between quantum systems such as electrons. Measuring two entangled electrons yields two outcomes, analogous to the numbers that face upward after you roll two dice. The quantum measurements’ outcomes can exhibit correlations stronger than any measurements of any classical, or nonquantum, systems can. Which die faces point upward can share only so much correlation, even if the dice hit each other.

einstein's q. riddle

Dice feature in the film’s explanations of entanglement. So does a variation on the shell game, in which one hides a ball under one of three cups, shuffles the cups, and challenges viewers to guess which cup is hiding the ball. The film derives its drama from the Cosmic Bell test. Bell tests are experiments crafted to show that classical physics can’t describe entanglement. Scientists recently enhanced Bell tests using light from quasars—ancient, bright, faraway galaxies. Mix astrophysics with quantum physics, and an edgy, pulsing soundtrack follows.

The Cosmic Bell test grew from a proposal by physicists at MIT and the University of Chicago. The coauthors include David Kaiser, a historian of science and a physicist on MIT’s faculty. Dave co-organized the premiere and the panel discussion that followed. The panel featured Dave; Paola Cappellaro, an MIT quantum experimentalist; Alan Guth, an MIT cosmologist who contributed to the Bell test; Calvin Leung, an MIT PhD student who contributed; Chris Schmidt, the film’s producer; and me. Brindha Muniappan, the Director of Education and Public Programs at the MIT Museum, moderated the discussion.

panel

think that the other panelists were laughing with me.

Brindha asked what challenges I face when explaining quantum physics, such as on this blog. Quantum theory wears the labels “weird,” “counterintuitive,” and “bizarre” in journalism, interviews, blogs, and films. But the thorn in my communicational side reflects quantum “weirdness” less than it reflects humanity’s self-limitation: Many people believe that we can’t grasp quantum physics. They shut down before asking me to explain.

Examples include a friend and Quantum Frontiers follower who asks, year after year, for books about quantum physics. I suggest literature—much by Dave Kaiser—he reads some, and we discuss his impressions. He’s learning, he harbors enough curiosity to have maintained this routine for years, and he has technical experience as a programmer. But he’s demurred, several times, along the lines of “But…I don’t know. I don’t think I’ll ever understand it. Humans can’t understand quantum physics, can we? It’s too weird.” 

Quantum physics defies many expectations sourced from classical physics. Classical physics governs how basketballs arch, how paint dries, how sunlight slants through your window, and other everyday experiences. Yet we can gain intuition about quantum physics. If we couldn’t, how could we solve problems and accomplish research? Physicists often begin solving problems by trying to guess the answer from intuition. We reason our way toward a guess by stripping away complications, constructing toy models, and telling stories. We tell stories about particles hopping from site to site on lattices, particles trapped in wells, and arrows flipping upward and downward. These stories don’t capture all of quantum physics, but they capture the essentials. After grasping the essentials, we translate them into math, check how far our guesses lie from truth, and correct our understanding. Intuition about quantum physics forms the compass that guides problem solving.

Growing able to construct, use, and mathematize such stories requires work. You won’t come to understand quantum theory by watching NOVA films, though films can prime you for study. You can gain a facility with quantum theory through classes, problem sets, testing, research, seminars, and further processing. You might not have the time or inclination to. Even if you have, you might not come to understand why quantum theory describes our universe: Science can’t necessarily answer all “why” questions. But you can grasp what quantum theory implies about our universe.

People grasp physics arguably more exotic than quantum theory, without exciting the disbelief excited by a grasp of quantum theory. Consider the Voyager spacecraft launched in 1977. Voyager has survived solar winds and -452º F weather, imaged planets, and entered interstellar space. Classical physics—the physics of how basketballs arch—describes much of Voyager’s experience. But even if you’ve shot baskets, how much intuition do you have about interstellar space? I know physicists who claim to have more intuition about quantum physics than about much classical. When astrophysicists discuss Voyager and interstellar space, moreover, listeners don’t fret that comprehension lies beyond them. No one need fret when quantum physicists discuss the electrons in us.

Fretting might not occur to future generations: Outreach teams are introducing kids to quantum physics through games and videos. Caltech’s Institute for Quantum Information and Matter has partnered with Google to produce QCraft, a quantum variation on Minecraft, and with the University of Southern California on quantum chess. In 2017, the American Physical Society’s largest annual conference featured a session called “Gamification and other Novel Approaches in Quantum Physics Outreach.” Such outreach exposes kids to quantum terminology and concepts early. Quantum theory becomes a playground to explore, rather than a source of intimidation. Players will grow up primed to think about quantum-mechanics courses not “Will my grade-point average survive this semester?” but “Ah, so this is the math under the hood of entanglement.”

qcraft 2

Sociology restricts people to thinking quantum physics weird. But quantum theory defies classical expectations less than it could. Measurement outcomes could share correlations stronger than the correlations sourced by entanglement. How strong could the correlations grow? How else could physics depart farther from classical physics than quantum physics does? Imagine the worlds governed by all possible types of physics, called “generalized probabilistic theories” (GPTs). GPTs form a landscape in which quantum theory constitutes an island, on which classical physics constitutes a hill. Compared with the landscape’s outskirts, our quantum world looks tame.

GPTs fall under the research category of quantum foundations. Quantum foundations concerns why the math that describes quantum systems describes quantum systems, reformulations of quantum theory, how quantum theory differs from classical mechanics, how quantum theory could deviate but doesn’t, and what happens during measurements of quantum systems. Though questions about quantum foundations remain, they don’t block us from intuiting about quantum theory. A stable owner can sense when a horse has colic despite lacking a veterinary degree.

Moreover, quantum-foundations research has advanced over the past few decades. Collaborations and tools have helped: Theorists have been partnering with experimentalists, such as on the Cosmic Bell test and on studies of measurement. Information theory has engendered mathematical tools for quantifying entanglement and other quantum phenomena. Information theory has also firmed up an approach called “operationalism.” Operationalists emphasize preparation procedures, evolutions, and measurements. Focusing on actions and data concretizes arguments and facilitates comparisons with experiments. As quantum-foundations research has advanced, so have quantum information theory, quantum experiments, quantum technologies, and interdisciplinary cross-pollination. Twentieth-century quantum physicists didn’t imagine the community, perspectives, and knowledge that we’ve accrued. So don’t adopt 20th-century pessimism about understanding quantum theory. Einstein grasped much, but today’s scientific community grasps more. Richard Feynman said, “I think I can safely say that nobody understands quantum mechanics.” Feynman helped spur the quantum-information revolution; he died before its adolescence. Besides, Feynman understood plenty about quantum theory. Intuition jumps off the pages of his lecture notes and speeches.

landscape

Landscape beyond quantum theory

I’ve swum in oceans and lakes, studied how the moon generates tides, and canoed. But piloting a steamboat along the Mississippi would baffle me. I could learn, given time, instruction, and practice; so can you learn quantum theory. Don’t let “weirdness,” “bizarreness,” or “counterintuitiveness” intimidate you. Humans can intuit quantum physics.

Chasing Ed Jaynes’s ghost

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

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

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

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

WashU

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

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

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

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

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

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

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

Who? asked the student behind the granola bars advertised as “Free study snacks—help yourself!” 

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

She turned to her computer. Can you spell that?

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

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

Library books

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

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

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

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

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

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

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

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

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

 

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

Theoretical physics has not gone to the dogs.

I was surprised to learn, last week, that my profession has gone to the dogs. I’d introduced myself to a nonscientist as a theoretical physicist.

“I think,” he said, “that theoretical physics has lost its way in symmetry and beauty and math. It’s too far from experiments to be science.”

The accusation triggered an identity crisis. I lost my faith in my work, bit my nails to the quick, and enrolled in workshops about machine learning and Chinese.

Or I might have, if all theoretical physicists pursued quantum gravity.

Quantum-gravity physicists attempt to reconcile two physical theories, quantum mechanics and general relativity. Quantum theory manifests on small length scales, such as atoms’ and electrons’. General relativity manifests in massive systems, such as the solar system. A few settings unite smallness with massiveness, such as black holes and the universe’s origin. Understanding these settings requires a unification of quantum theory and general relativity.

Try to unify the theories, and you’ll find yourself writing equations that contain infinities. Such infinities can’t describe physical reality, but they’ve withstood decades of onslaughts. For guidance, many quantum-gravity theorists appeal to mathematical symmetries. Symmetries, they reason, helped 20th-century particle theorists predict experimental outcomes with accuracies better than any achieved with any other scientific theory. Perhaps symmetries can extend particle physics to a theory of quantum gravity.

Some physicists have criticized certain approaches to quantum gravity, certain approaches to high-energy physics more generally, and the high-energy community’s philosophy and sociology. Much criticism has centered on string theory, according to which our space-time has up to 26 dimensions, most too small for you to notice. Critics include Lee Smolin, the author of The Trouble with Physics, Peter Woit, who blogs on Not Even Wrong, and Sabine Hossenfelder, who published Lost in Math this year. This article contains no criticism of their crusade. I see merit in arguments of theirs, as in arguments of string theorists.

Science requires criticism to progress. So thank goodness that Smolin, Woit, Hossenfelder, and others are criticizing string theory. Thank goodness that the criticized respond. Thank goodness that debate rages, like the occasional wildfire needed to maintain a forest’s health.

The debate might appear to impugn the integrity of theoretical physics. But quantum gravity constitutes one pot in the greenhouse of theoretical physics. Theoretical physicists study lasers, star formation, atomic clocks, biological cells, gravitational waves, artificial materials, and more. Theoretical physicists are explaining, guiding, and collaborating on experiments. So many successes have piled up recently, I had trouble picking examples for this article. 

One example—fluctuation relations—I’ve blogged about beforeThese equalities generalize the second law of thermodynamics, which illuminates why time flows in just one direction. Fluctuation relations also provide a route to measuring an energetic quantity applied in pharmacology, biology, and chemistry. Experimentalists have shown, over the past 15 years, that fluctuation relations govern RNA, DNA, electronic systems, and trapped ions (artificial atoms). 

Second, experimentalists are exercising, over quantum systems, control that physicists didn’t dream of decades ago. Harvard physicists can position over 50 atoms however they please, using tweezers formed from light. Google has built a noisy quantum computer of 72 superconducting qubits, circuits through which charge flows without resistance. Also trapped ions, defects in diamonds, photonics, and topological materials are breaking barriers. These experiments advance partially due to motivation from theorists and partially through collaborations with theorists. In turn, experimental data guide theorists’ explanations and our proposals of experiments.

In one example, theorists teamed with experimentalists to probe quantum correlations spread across space and time. In another example, theorists posited a mechanism by which superconducting qubits interact with a hot environment. Other illustrations from the past five years include discrete time crystals, manybody scars, magic-angle materials, and quantum chaos. 

These collaborations even offer hope for steering quantum gravity with experiments. Certain quantum-gravity systems share properties with certain many-particle quantum systems. This similarity, we call “the AdS/CFT duality.” Experimentalists have many-particle quantum systems and are stretching those systems toward the AdS/CFT regime. Experimental results, with the duality, might illuminate where quantum-gravity theorists should and shouldn’t search. Perhaps no such experiments will take place for decades. Perhaps AdS/CFT can’t shed light on our universe. But theorists and experimentalists are partnering to try.

These illustrations demonstrate that theoretical physics, on the whole, remains healthy, grounded, and thriving. This thriving is failing to register with part of the public. Evidence thwacked me in the face last week, as explained at the start of this article. The Wall Street Journal published another example last month: John Horgan wrote that “physics, which should serve as the bedrock of science, is in some respects the most troubled field of” science. The evidence presented consists of one neighborhood in the theoretical fraction of the metropolis of physics: string and multiverse models.

Horgan’s article reflects decades of experience in science journalism, a field I respect. I sympathize, moreover, with those who interface so much with quantum gravity, the subfield appears to eclipse the rest of theoretical physics. Horgan was reviewing books by Stephen Hawking and Martin Rees, who discuss string and multiverse models. Smolin, Woit, Hossenfelder, and others garner much press, which they deserve: They provoke debate and articulate their messages eloquently. Such press can blot out, say, profiles of the theoretical astrophysicists licking their lips over gravitational-wave data.

If any theory bears flaws, those flaws need correcting. But most theoretical physicists don’t pursue quantum gravity, let alone string theory. Any flaws of string theory do not mar all theoretical physics. These points need a megaphone, because misconceptions about theoretical physics endanger society. First, companies need workers who have technical skills and critical reasoning. Both come from training in theoretical physics. Besmirching theoretical physics can divert students from programs that can benefit the economy and nurture thoughtful citizens.1 

Second, some nonscientists are attempting to discredit the scientific community for political gain. Misconceptions about theoretical physics can appear to support these nonscientists’ claims. The ensuing confusion can lead astray voters and parents who face choices about vaccination, global health, national security, and budget allocations.

Last week, I heard that my profession has wandered too far from experiments. Hours earlier, I’d skyped with an experimentalist with whom I’m collaborating. A disconnect separates the reality of theoretical physicists from impressions harbored by part of the public. Let’s clear up the misconceptions. Theoretical physics, as a whole, remains healthy, grounded, and thriving.

 

 

1Nurturing thoughtful citizens takes also humanities, social-sciences, language, and arts programs.

Doctrine of the (measurement) mean

Don’t invite me to dinner the night before an academic year begins.

You’ll find me in an armchair or sitting on my bed, laptop on my lap, journaling. I initiated the tradition the night before beginning college. I take stock of the past year, my present state, and hopes for the coming year.

Much of the exercise fosters what my high-school physics teacher called “an attitude of gratitude”: I reflect on cities I’ve visited, projects firing me up, family events attended, and subfields sampled. Other paragraphs, I want off my chest: Have I pushed this collaborator too hard or that project too little? Miscommunicated or misunderstood? Strayed too far into heuristics or into mathematical formalisms?

If only the “too much” errors, I end up thinking, could cancel the “too little.”

In one quantum-information context, they can.

Seesaw

Imagine that you’ve fabricated the material that will topple steel and graphene; let’s call it a supermetatopoconsulator. How, you wonder, do charge, energy, and particles move through this material? You’ll learn by measuring correlators.

A correlator signals how much, if you poke this piece here, that piece there responds. At least, a two-point correlator does: \langle A(0) B(\tau) \rangle. A(0) represents the poke, which occurs at time t = 0. B(\tau) represents the observable measured there at t = \tau. The \langle . \rangle encapsulates which state \rho the system started in.

Condensed-matter, quantum-optics, and particle experimentalists have measured two-point correlators for years. But consider the three-point correlator \langle A(0) B(\tau) C (\tau' ) \rangle, or a k-point \langle \underbrace{ A(0) \ldots M (\tau^{(k)}) }_k \rangle, for any k \geq 2. Higher-point correlators relate more-complicated relationships amongst events. Four-pointcorrelators associated with multiple times signal quantum chaos and information scrambling. Quantum information scrambles upon spreading across a system through many-body entanglement. Could you measure arbitrary-point, arbitrary-time correlators?

New material

Supermetatopoconsulator (artist’s conception)

Yes, collaborators and I have written, using weak measurements. Weak measurements barely disturb the system being measured. But they extract little information about the measured system. So, to measure a correlator, you’d have to perform many trials. Moreover, your postdocs and students might have little experience with weak measurements. They might not want to learn the techniques required, to recalibrate their detectors, etc. Could you measure these correlators easily?

Yes, if the material consists of qubits,2 according to a paper I published with Justin Dressel, José Raúl González Alsonso, and Mordecai Waegell this summer. You could build such a system from, e.g., superconducting circuits, trapped ions, or quantum dots.

You can measure \langle \underbrace{ A(0) B (\tau') C (\tau'') \ldots M (\tau^{(k)}) }_k \rangle, we show, by measuring A at t = 0, waiting until t = \tau', measuring B, and so on until measuring M at t = \tau^{(k)}. The t-values needn’t increase sequentially: \tau'' could be less than \tau', for instance. You’d have to effectively reverse the flow of time experienced by the qubits. Experimentalists can do so by, for example, flipping magnetic fields upside-down.

Each measurement requires an ancilla, or helper qubit. The ancilla acts as a detector that records the measurement’s outcome. Suppose that A is an observable of qubit #1 of the system of interest. You bring an ancilla to qubit 1, entangle the qubits (force them to interact), and look at the ancilla. (Experts: You perform a controlled rotation on the ancilla, conditioning on the system qubit.)

Each trial yields k measurement outcomes. They form a sequence S, such as (1, 1, 1, -1, -1, \ldots). You should compute a number \alpha, according to a formula we provide, from each measurement outcome and from the measurement’s settings. These numbers form a new sequence S' = \mathbf{(} \alpha_S(1), \alpha_S(1), \ldots \mathbf{)}. Why bother? So that you can force errors to cancel.

Multiply the \alpha’s together, \alpha_S(1) \times \alpha_S(1) \times \ldots, and average the product over the possible sequences S. This average equals the correlator \langle \underbrace{ A(0) \ldots M (\tau^{(k)}) }_k \rangle. Congratulations; you’ve characterized transport in your supermetatopoconsulator.

Success

When measuring, you can couple the ancillas to the system weakly or strongly, disturbing the system a little or a lot. Wouldn’t strong measurements perturb the state \rho whose properties you hope to measure? Wouldn’t the perturbations by measurements one through \ell throw off measurement \ell + 1?

Yes. But the errors introduced by those perturbations cancel in the average. The reason stems from how we construct \alpha’s: Our formula makes some products positive and some negative. The positive and negative terms sum to zero.

Balance 2

The cancellation offers hope for my journal assessment: Errors can come out in the wash. Not of their own accord, not without forethought. But errors can cancel out in the wash—if you soap your \alpha’s with care.

 

1and six-point, eight-point, etc.

2Rather, each measured observable must square to the identity, e.g., A^2 = 1. Qubit Pauli operators satisfy this requirement.

 

With apologies to Aristotle.