Ten lessons I learned from John Preskill

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

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

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

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

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

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

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

…the mention of whom in my CQIQC talk invited…

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

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

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

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

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

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

and

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

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

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

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

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

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

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

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

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

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

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

Congratulations on your Bell Prize, John.

¹Really, the dissipated work.

²Really, hardcore bosons.