Balancing the tradeoff

So much to do, so little time. Tending to one task is inevitably at the cost of another, so how does one decide how to spend their time? In the first few years of my PhD, I balanced problem sets, literature reviews, and group meetings, but at the detriment to my hobbies. I have played drums my entire life, but I largely fell out of practice in graduate school. Recently, I made time to play with a group of musicians, even landing a couple gigs in downtown Austin, Texas, “live music capital of the world.” I have found attending to my non-physics interests makes my research hours more productive and less taxing. Finding the right balance of on- versus off-time has been key to my success as my PhD enters its final year.

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

The author doing his part to “keep Austin weird” by playing the drums dressed as grackle (note the beak), the central-Texas bird notorious for overrunning grocery store parking lots.
Balancing research interests: Trapping a glass microsphere with optical tweezers.
Balancing research interests: Visualizing the time evolution of four different QCA rules.

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

Classical cellular automata. Left: rule 90 producing the fractal Sierpiński’s triangle. Middle: rule 30 can be used to generate random numbers. Right: rule 110 is capable of universal computation.

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

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

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

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

Visualizing mutual information networks. Left: A Goldilocks-QCA generated network. Right: a random network.

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

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

I wish you a Charles River

Three-and-a-quarter years ago, I was on a subway train juddering along the tracks. I gripped my suitcase tightly and—knowing myself—likely gripped a physics paper, too, so that I could read during the trip. I was moving, for my postdoctoral fellowship, to Cambridge from Pasadena, where I’d completed my PhD.

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

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

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

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

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

Entangled Fields and Post-Anthropocene Computation: Quantum Perspectives for a Healthy Planet

Natalie Klco
Institute for Quantum Information and Matter (IQIM) and Walter Burke Institute for Theoretical Physics
California Institute of Technology, Pasadena CA 91125, USA, Earth1
November 7, 2021 (COP26 Day 8)

If a quantum field is replaced with lower complexity versions of itself, the field systematically falls apart into ever smaller pieces. Rather than permeating all of space, the entanglement—a unique form of correlations tying together the quantum world—abruptly vanishes2. Where once there was global connection now devolves into fragments. If the biological fields of our planet are replaced with lower-complexity versions of themselves, analogous collapse ensues. The natural world requires and celebrates complexity.

Visual representation of complexity reduction in biological fields from (left) diverse coherent ecosystems with phenomena across many length scales to (right) fragmented precision monocultures with phenomena in limited bandwidth. Analogous complexity reductions in quantum fields cause harsh decoherence.
(Images by Ruvim Miksanskiy and NASA Earth Observatory Landsat)

Humans have a fascinating relationship with nature’s complexity—they love it when they understand it, and tend to destroy it when they don’t: Maxwellian demons reducing complexity rather than entropy, with the reduction scaling inversely with insight. This is most often not malicious at the beginning; we enjoy understanding how things work and modifying them to our desires. If we don’t understand something, an effective way to learn is to simplify it, dissect and put it back together, sometimes with fewer pieces so the purpose and importance of each piece can be deduced. As we become comfortable with the basic elements, embellishments can be added. This is how elaborate modern technology has been developed; this is how discoveries in abstract mathematics are made; this is how symphonies are composed. While valuable for developments of human creation, this perspective is dangerous when applied to societal structures that now glorify the simple homogeneous monoculture, both of the Earth and of its inhabitants.

Naïvely, uncontrollable pursuit of understanding and quickly adaptable manipulation skills, along with systematic analysis and pattern recognition capabilities to deduce large-scale and long-time trends, are logical characteristics to incorporate in an intellectually-powerful-but-otherwise-non-remarkable species within your ecosystem. Such a species would be able to recognize the occasional imbalance in nature and to provide a slight rectifying tilt. Not only could they do so, but they are designed to enjoy it! “The pleasure of finding things out” followed by the satisfaction of influencing the world external.

The naïvety of this suggested ecological role for humans overlooks the reality that our society is increasingly being driven by forces programmed to incentivize actions knowingly contrary to personal, community, and planetary best interests. Though we tend to try to put things back together, the process is often slow and filled with hubris for control. Analogous to the qubit becoming a natural tool for entanglement restoration, we reintroduce locally extirpated phenomena and species as restricted tools of ecosystem recovery: from natural airflow that better dissipates pathogens, to beavers gracefully orchestrating water distribution and the construction of entire ecosystems, to wolves creating trophic cascades that erupt in species diversity and even stabilize geographic features of the land, to earthworms aerating the soil, recycling nutrients, and supporting the diverse microbial life enveloping the Earth3. Nature is full of astoundingly fascinating examples of collaboratively created cycles, thoroughly intertwining the lives of species throughout the taxonomic ranks. Though the above naïvety identifies one theoretically plausible respectable function of the human species, we have yet to mature into any truly valuable ecological role. If humans suddenly disappeared, would any (non-domesticated) species be interested in fighting for our reintroduction? Or would there simply be…relief?

It is not a winning strategy for our understanding4 to be a necessary condition for “allowing” natural processes to occur. Though humans have become devastatingly linear creatures5, we fuel a vicious cycle of destruction, appreciation, and monetized mono-restoration. Dangerously, our efficiency in step-one often breaks this cycle, too. From free-flowing rivers to the communication networks of mycorrhizal fungi in old-growth forests, we are losing vital information of healthy ecosystems faster than they can be appreciated. How will we know what actions help to restore nature when we have lost all examples of her complex beauty? What will we do when she is gone?


As I modify my life to reflect growing concerns, the following perspective is important:

Changing the system, not perfecting our own lives, is the point. “Hypocrisy” is the price of admission in this battle. –Bill McKibben [NYT, 2016]

I will keep riding my bike for primary transportation (fun, healthy, and responsible!), adding plants to my diet (tasty, healthy, and responsible!), and showering by the light pollution through my bathroom window. I do these things not with the illusion that they are impactful, but to keep stoked an internal fire focused on brainstorming ways that a quantum physicist/musician could convince the powerful humans to make decisions that reprogram our society to calm, rather than cause, the storms spiraling our planet out of balance.


Results (so far):

Quantum physicists have been forced to realize for decades how ignoring the structure of nature can leave you struggling exponentially far from your goals. The way that nature processes information is fundamentally different than the way that we currently do…and her techniques are often exponentially superior. In the same way that we are turning to nature for solutions in simulating the quantum world, so too must we turn to nature for solutions in planetary stability. We are not going to technologically innovate ourselves out of this problem—nature has a multi-million-year head start in her R&D investments. While there are absolutely technologies (both quantum and classical) that may make the transition more rapid and comfortable, if technological solutions worked, we would have innovated ourselves out of this predicament a half-century ago when oil companies with planetary-sized spheres of influence were well-informed of the situation.

Right now, we are being asked by the Earth, still relatively kindly, to stop; to stop haphazardly taking apart her cyclic and entangled systems; to let nature heal the reductive wounds caused by our curiosity and by the endless extraction of our growth economy incompatible with a finite planet; to relish when her healthy wholeness leads to a complexity that boggles our minds; to provide planetary reprieve with a global performance of John Cage’s silent composition, 4’33”, hopefully temporally dilated; to actively stand aside. While we do so, we can peacefully ponder and reframe the vision of what our lives on this Earth should be.

In the quantum community, we have already developed the necessary mentality. We daily envision a more natural way of interacting with the world. This vision has successfully been passed through multiple generations of researchers—communicable inspiration being an essential ingredient for developments that began a century ago and may take a century more to come to full fruition. In one case, we must break from a past driven by exploitation, developed in a time when the fallacy of infinite resources was a functional approximation. In the other case, we must create an entirely new programming language built on the laws of quantum mechanics and must develop unprecedented levels of precision control necessary to compute with nature’s quantum bits. One of these challenges should be easier than the other.

In artistic performance, learning a new piece can feel like learning a new way of living. To engrain and genuinely express a new perspective, it can be helpful to work at multiple levels of abstraction. This assures that all sides of your being—intellectual, emotional, linguistic, kinesthetic, etc.—are evenly integrated, optimized for an honest portrayal of the artistic vision. In the context of planetary fragmentation decimating ecosystem coherence, quantum information provides one such valuable abstraction.

We have a story to tell that parallels, from the quantum world, our current planetary challenges. Our story is one of past destructive reduction and an ongoing pursuit of redemption reintroducing fundamental pieces of nature back into our calculations. Quantum physicists have already been through the exponentially diminished darkness and are joyously engaged in creating a future where nature’s complexities are respected and honored. We have turned phenomena famously lamented for their tortuously tangled interpretations into cherished and invaluable resources capable of achieving far more than their simplified predecessors. This endeavor is requiring (and achieving!) extensive global coordination and institutional support from local to federal levels.

Our community has learned to celebrate the complexity of the natural world. To share that vision is something important we can do. In this context, quantum physicists are natural “complexity therapists”. As society rewilds the land and reconnects our lives to nature, we can help usher in an era of corporately treasuring the invaluable resources of diverse and complex natural processes, not only for computational advantage but for the survival of all remaining life.

1. Affiliation provided for context. The views and opinions expressed herein are solely those of the author and do not reflect the official policy or position of Caltech or affiliated institutes.
2. The following reflections accompany recent research quantifying entanglement in the scalar field vacuum [1][2][3].
3. Fun Fact: Ancient Egypt imposed a death penalty for tampering with the Earth Worms!
4. and subsequent ability to secure legislative/judicial protections
5. e.g., plastic, million-year oil and ground water resources consumed in a generation, carcass removal (both plant and animal) systematically depleting nutrients from ecosystems that have specific mechanisms for nutrient retention and reintegration, etc.

Quantum estuary

Tourism websites proclaim, “There’s beautiful…and then there’s Santa Barbara.” I can’t accuse them of hyperbole, after living in Santa Barbara for several months. Santa Barbara’s beauty manifests in its whitewashed buildings, capped with red tiles; in the glint of sunlight on ocean wave; and in the pockets of tranquility enfolded in meadows and copses. An example lies about an hour’s walk from the Kavli Institute for Theoretical Physics (KITP), where I spent the late summer and early fall: an estuary. According to National Geographic, “[a]n estuary is an area where a freshwater river or stream meets the ocean.” The meeting of freshwater and saltwater echoed the meeting of disciplines at the KITP.

The KITP fosters science as a nature reserve fosters an ecosystem. Every year, the institute hosts several programs, each centered on one scientific topic. A program lasts a few weeks or months, during which scientists visit from across the world. We present our perspectives on the program topic, identify intersections of interests, collaborate, and exclaim over the ocean views afforded by our offices.

Not a bad office view, eh?

From August to October, the KITP hosted two programs about energy and information. The first program was called “Energy and Information Transport in Non-Equilibrium Quantum Systems,” or “Information,” for short. The second program was called “Non-Equilibrium Universality: From Classical to Quantum and Back,” or “Universality.” The programs’ topics and participant lists overlapped, so the KITP merged “Information” and “Universality” to form “Infoversality.” Don’t ask me which program served as the saltwater and which as the fresh.

But the mingling of minds ran deeper. Much of “Information” centered on quantum many-body physics, the study of behaviors emergent in collections of quantum particles. But the program introduced many-body quantum physicists to quantum thermodynamics and vice versa. (Quantum thermodynamicists re-envision thermodynamics, the Victorian science of energy, for quantum, small, information-processing, and far-from-equilibrium systems.) Furthermore, quantum thermodynamicists co-led the program and presented research at it. Months ago, someone advertised the program in the quantum-thermodynamics Facebook group as an activity geared toward group members. 

The ocean of many-body physics was to meet the river of quantum thermodynamics, and I was thrilled as a trout swimming near a hiker who’s discovered cracker crumbs in her pocket. 

A few of us live in this estuary, marrying quantum thermodynamics and many-body physics. I waded into the waters in 2016, by codesigning an engine (the star of Victorian thermodynamics) formed from a quantum material (studied in many-body physics). We can use tools from one field to solve problems in the other, draw inspiration from one to design questions in the other, and otherwise do what the United States Food and Drug Administration recently announced that we can do with COVID19 vaccines: mix and match.

It isn’t easy being interdisciplinary, so I wondered how this estuary would fare when semi-institutionalized in a program. I collected observations like seashells—some elegantly molded, some liable to cut a pedestrian’s foot, and some both.

Across the street from the KITP.

A sand dollar washed up early in the program, as I ate lunch with a handful of many-body physicists. An experimentalist had just presented a virtual talk about nanoscale clocks, which grew from studies of autonomous quantum clocks. The latter run on their own, without needing any external system to wind or otherwise control them. You’d want such clocks if building quantum engines, computers, or drones that operate remotely. Clocks measure time, time complements energy mathematically in physics, and thermodynamics is the study of energy; so autonomous quantum clocks have taken root in quantum thermodynamics. So I found myself explaining autonomous quantum clocks over sandwiches. My fellow diners expressed interest alongside confusion.

A scallop shell, sporting multiple edges, washed up later in the program: Many-body physicists requested an introduction to quantum thermodynamics. I complied one afternoon, at a chalkboard in the KITP’s outdoor courtyard. The discussion lasted for an hour, whereas most such conversations lasted for two. But three participants peppered me with questions over the coming weeks.

A conch shell surfaced, whispering when held to an ear. One program participant, a member of one community, had believed the advertising that had portrayed the program as intended for his cohort. The portrayal didn’t match reality, to him, and he’d have preferred to dive more deeply into his own field.

I dove into a collaboration with other KITPists—a many-body project inspired by quantum thermodynamics. Keep an eye out for a paper and a dedicated blog post.

A conference talk served as a polished shell, reflecting light almost as a mirror. The talk centered on erasure, a process that unites thermodynamics with information processing: Imagine performing computations in math class. You need blank paper (or the neurological equivalent) on which to scribble. Upon computing a great deal, you have to erase the paper—to reset it to a clean state. Erasing calls for rubbing an eraser across the paper and so for expending energy. This conclusion extends beyond math class and paper: To compute—or otherwise process information—for a long time, we have to erase information-storage systems and so to expend energy. This conclusion renders erasure sacred to us thermodynamicists who study information processing. Erasure litters our papers, conferences, and conversations.

Erasure’s energy cost trades off with time: The more time you can spend on erasure, the less energy you need.1 The conference talk explored this tradeoff, absorbing the quantum thermodynamicist in me. A many-body physicist asked, at the end of the talk, why we were discussing erasure. What quantum thermodynamicists took for granted, he hadn’t heard of. He reflected back at our community an image of ourselves from an outsider’s perspective. The truest mirror might not be the flattest and least clouded.

The author, wearing a KITP hat, not far from either estuary—natural or quantum.

Plants and crustaceans, mammals and birds, grow in estuaries. Call me a bent-nosed clam, but I prefer a quantum estuary to all other environments. Congratulations to the scientists who helped create a quantum estuary this summer and fall, and I look forward to the harvest.

1The least amount of energy that erasure can cost, on average over trials, is called Landauer’s bound. You’d pay this bound’s worth of energy if you erased infinitely slowly.

My 100th anniversary with Quantum Frontiers

Queen Elizabeth II celebrated the 60th year of her reign in 2012. I was working as a research assistant at Lancaster University, in northern England. The university threw a tea party, which I attended with a friend. She wrangled me into donning a party hat decorated with the Union Jack. Sixtieth anniversaries, I learned that year, are associated with diamond.

I had trouble finding what 100th anniversaries are associated with—I presume because few queens and couples reach their centennials. But I dug up an answer (all hail the Internet): bone. This post marks my bone anniversary with Quantum Frontiers—my 100th article.

To everyone who’s journeyed with me since article number one, or joined me partway through, or tolerating my writing for the first time now: Thank you. The opportunity to connect with so many people, from undergraduates to art teachers to quantum-information experts to librarians, has been a blessing. I’ve been surprised at, and grateful for, your sharing of what this blog means to you. You’ve reached out during campus visits, at American Physical Society conferences, in emails, and on Twitter. Thank you for enriching my writing life.

A virtual meetup coordinated by Quantum Frontiers readers

The journey began in mid-May 2013, when I signed my soul to Caltech’s PhD program. Fellow blogger John Preskill1 agreed to supervise me for five years. My first blog post said, “For five years, I will haunt this blog. (Spiros [the creator and gatekeeper of Quantum Frontiers] will haunt me if I don’t haunt it.) I’ll try to post one article per month.” I’ve posted one article per month since then. 

Since then, much has transpired. Career-wise, I finished a Master’s degree; earned a PhD; completed a postdoctoral fellowship at the Harvard-Smithsonian Institute for Theoretical Atomic, Molecular, and Optical Physics; committed to doing physics at the National Institute for Science and Technology; stumbled over several acronyms; and founded a research group. Outside of work, I married off my best friend, fell in love and got married myself, lost two grandmothers, and wrote a book. I found myself in more countries than I can count on one hand, in more US states than countries, and jet-lagged for more hours than I care to recall. Quantum Frontiers has served as a diary and a taskmaster, challenging me to find and crystallize meaning in my experiences.

After presenting a toast at my best friend’s wedding—which, because my best friend married a former scientist, almost doubled as a conference

Although professional and personal affairs have had cameos, learning and research have starred in these 100 articles. My research has evolved over the past eight years, not only as recorded on, but also partially thanks to, this blog. Physicists lionize imagination, but some imaginings have no place even in physics papers. This blog serves as a home for the poetry, the puns, the evocative typos, and the far-fetched connections that Physical Review wouldn’t publish. But nurturing whimsy that Physical Review wouldn’t publish fosters whimsy that Physical Review would. Blogging, I’ve found, promotes creativity that enhances research.

My research dwelled in Abstract-Theory Land in 2013—pure quantum-information-theoretic thermodynamics. Caltech bridged my research to the real physical world: condensed matter; atomic molecular, and optical physics; and chemistry. The transformation continued during my postdoc, producing two experimental papers and initiating three more. I don’t think that the metamorphosis will progress, and I keep a foot in abstract theory. But if I awake one morning from troubled dreams, finding myself changed into an experimentalist or an engineer, you’ll be among the first to know. 

I’ve come to know you a little over the past eight years. Many of you like listicles, according to WordPress statistics. You like former Quantum Frontiers blogger Shaun Maguire more than you like me; his most popular article has logged about 142,000 views, whereas mine has logged about 18,000. That’s ok; I’ve never been the popular kid, and I’m a Shaun Maguire fan, too. But, beyond Shaun and listicles, what draws you has surprised Spiros, John, and me. John anticipated that the article “Theoretical physics has not gone to the dogs” would stir up conversation (Do you think it’ll offend anyone? I asked. I hope so, he replied), but other articles have taken off on Twitter unexpectedly. Maybe we’ll understand you better another 100 articles down the line.

Blogging offered me the freedom to recognize and celebrate the steampunk aesthetic of quantum thermodynamics, my field of research. My first PhD student gifted me this adorable steampunk owl sculpture for my birthday this year.

My first blog post contained a quote from Goethe’s Faust. The play opens with a poet reminiscing about his earlier years: “Nothing I had; and yet, enough for youth—/ delight in fiction, and the thirst for truth.” I still delight in fiction, as attested to by a 2020 post about the magical realist Gabriel García Marquez. I’d better thirst for truth no less, now that experimental collaborators are grounding me in reality. Partnering truth with fiction, so that each enhances the other, delights me most—and encapsulates what I aim for on Quantum Frontiers. As I wrote in May 2013, invoking the thirst for truth: Drink with me. I’ll drink a cup of tea to another 100 blog posts.

1Who hasn’t blogged much recently. How about it, John? 

How a liberal-arts education has enhanced my physics research

I attended a liberal-arts college, and I reveled in the curriculum’s breadth. My coursework included art history, psychology, biology, economics, computer science, German literature, archaeology, and chemistry. My major sat halfway between the physics major and the create-your-own major; the requirements consisted mostly of physics but included math, philosophy, and history. By the end of college, I’d determined to dive into physics. So I undertook a physics research assistantship, enlisted in a Master’s program and then a PhD program, and became a theoretical physicist. I’m now building a physics research group that spans a government institute and the University of Maryland. One might think that I became a physicist despite my art history and archaeology. 

My liberal-arts education did mortify me a little as I pursued my Master’s degree. Most of my peers had focused on physics, mathematics, and computer science while I’d been reading Aristotle. They seemed to breeze through coursework that I clawed my way through. I still sigh wistfully over math courses, such as complex analysis, that I’ve never taken. Meanwhile, a debate about the liberal arts has been raging across the nation. Debt is weighing down recent graduates, and high-school students are loading up on STEMM courses. Colleges are cutting liberal-arts departments, and educational organizations are broadcasting the value of liberal-arts educations.

I’m not an expert in public policy or school systems; I’m a physicist. As a physicist, I’m grateful for my liberal-arts education. It’s enhanced my physics research in at least five ways.

(1) I learned to seek out, and take advantage of, context. Early in my first German-literature course, I’d just completed my first reading assignment. My professor told my class to fetch out our books and open them to the beginning. A few rustles later, we held our books open to page one of the main text. 

No, no, said my professor. Open your books to the beginning. Did anyone even look at the title page?

We hadn’t, we admitted. We’d missed a wealth of information, as the book contained a reproduction of an old title page. Publishers, fonts, and advertisement styles have varied across the centuries and the globe. They, together with printing and reprinting dates, tell stories about the book’s origin, popularity, role in society, and purposes. Furthermore, a frontispiece is worth a thousand words, all related before the main text begins. When my class turned to the main text, much later in the lecture, we saw it in a new light. Context deepens and broadens our understanding.

When I read a physics paper, I start at the beginning—the true beginning. I note the publication date, the authors, their institutions and countries, and the journal. X’s lab performed the experiment reported on? X was the world’s expert in Y back then but nursed a bias against Z, a bias later proved to be unjustified. So I should aim to learn from the paper about Y but should take statements about Z with a grain of salt. Seeking and processing context improves my use of physics papers, thanks to a German-literature course.

(2) I learned argumentation. Doing physics involves building, analyzing, criticizing, and repairing arguments. I argue that mathematical X models physical system Y accurately, that an experiment I’ve proposed is feasible with today’s technology, and that observation Z supports a conjecture of mine. Physicists also prove mathematical statements deductively. I received proof-writing lessons in a math course, halfway through college. One of the most competent teachers I’ve ever encountered taught the course. But I learned about classes of arguments and about properties of arguments in a philosophy course, Informal Logic. 

There, I learned to distinguish deduction from inference and an argument’s validity and soundness from an argument’s strength and cogency. I learned strategies for proving arguments and learned fallacies to criticize. I came to respect the difference between “any” and “every,” which I see interchanged in many physics papers. This philosophical framework helps me formulate, process, dissect, criticize, and correct physics arguments. 

For instance, I often parse long, dense, technical proofs of mathematical statements. First, I identify whether the proof strategy is reductio ad absurdum, proof by counterexample, or another strategy. Upon identifying the overarching structure, I can fill my understanding with details. Additionally, I check proofs by students, and I respond to criticisms of my papers by journal referees. I could say, upon reading an argument, “Something feels a bit off, and it’s sort of like the thing that felt a bit off in that paper I read last Tuesday.” But I’d rather group the argument I’m given together with arguments I know how to tackle. I’d rather be able to say, “They’re straw-manning my argument” or “That argument begs the question.” Doing so, I put my finger on the problem and take a step toward solving it.

(3) I learned to analyze materials to bits, then extract meaning from the analysis. English and German courses trained me to wring from literature every drop of meaning that I could discover. I used to write one to three pages about a few-line quotation. The analysis would proceed from diction and punctuation to literary devices; allusions; characters’ relationships with each other, themselves, and nature; and the quotation’s role in the monograph. Everything from minutia to grand themes required scrutiny, according to the dissection technique I trained in. Every pincer probe lifted another skein of skin or drew aside another tendon, offering deeper insights into the literary work. I learned to find the skeins to lift, lift them in the right direction, pinpoint the insights revealed, and integrate the insights into a coherent takeaway.

This training has helped me assess and interpret mathematics. Physicists pick a physical system to study, model the system with equations, and solve the equations. The next two steps are intertwined: evaluating whether one solved the equations correctly and translating the solution into the physical system’s behavior. These two steps necessitate a dissection of everything from minutia to grand themes: Why should this exponent be 4/5, rather than any other number? Should I have expected this energy to depend on that length in this way? Is the physical material aging quickly or resisting change? These questions’ answers inform more-important questions: Who cares? Do my observations shed light worth anyone’s time, or did I waste a week solving equations no one should care about?

To answer all these questions, I draw on my literary training: I dissect content, pinpoint insights, and extract meaning. Having performed this analysis in literature courses facilitates an arguably deeper analysis than my physics training did: In literature courses, I had to organize my thoughts and articulate them in essays. This process revealed holes in my argumentation, as well as connections that I’d overlooked. In contrast, a couple of lines in my physics homework earned full marks. The critical analysis of literature has deepened my assessment of solutions’ correctness, physical interpretation of mathematics, and extraction of meaning from solutions. 

(4) I learned what makes a physicist a physicist. In college, I had a friend who was studying applied mathematics and economics. Over dinner, he described a problem he’d encountered in his studies. I replied, almost without thinking, “From a physics perspective, I’d approach the problem like this.” I described my view, which my friend said he wouldn’t have thought of. I hadn’t thought of myself, and of the tools I was obtaining in the physics department, the way I did after our conversation. 

Physics involves a unique toolkit,1 set of goals, and philosophy. Physicists identify problems, model them, solve them, and analyze the results in certain ways. Students see examples of these techniques in lectures and practice these techniques for homework. But, as a student, I rarely heard articulations of the general principles that underlay the examples scattered across my courses like a handful of marbles across a kitchen floor. Example principles include, if you don’t understand an abstract idea, construct a simple example. Once you’ve finished a calculation, check whether your answer makes sense in the most extreme scenarios possible. After solving an equation, interpret the solution in terms of physical systems—of how particles and waves move and interact. 

I was learning these techniques, in college, without realizing that I was learning them. I became conscious of the techniques by comparing the approach natural to me with the approach taken in another discipline. Becoming conscious of my toolkit enabled me to wield it more effectively; one can best fry eggs when aware that one owns a spatula. The other disciplines at my liberal-arts college served as a foil for physics. Seeing other disciplines, I saw what makes physics physics—and improved my ability to apply my physics toolkit.

(5) I learned to draw connections between diverse ideas. Senior year of high school, my courses extended from physics to English literature. One might expect such a curriculum to feel higgledy-piggledy, but I found threads that ran through all my courses. For instance, I practiced public speaking in Reasoning, Research, and Rhetoric. Because I studied rhetoric, my philosophy teacher turned to me for input when introducing the triumvirate “thesis, antithesis, synthesis.”2 The philosophy curriculum included the feminist essay “If Men Could Menstruate,” which complemented the feminist book Wide Sargasso Sea in my English-literature course. In English literature, I learned that Baldassare Castiglione codified how Renaissance noblemen should behave, in The Book of the Courtier. The author’s name was the answer to the first question on my AP Modern European History exam. My history course covered Isaac Newton and Gottfried Wilhelm Leibniz, who invented calculus during the 17th century. I leveraged their discoveries in my calculus course, which I applied in my physics course. My physics teacher hoped that his students would solve the world’s energy problems—perhaps averting the global thermonuclear war that graced every debate in my rhetoric course (“If you don’t accept my team’s policy, then X will happen, leading to Y, leading to Z, which will cause a global thermonuclear war”). 

Threads linked everything across my liberal-arts education; every discipline featured an idea that paralleled an idea in another discipline. Finding those parallels grew into a game for me, a game that challenged my creativity. Cultivating that creativity paid off when I began doing physics research. Much of my research has resulted from finding, in one field, a concept that resembles a concept in another field. I smash the ideas together to gain insight into each discipline from the other discipline’s perspective. For example, during my PhD studies, I found a thread connecting the physics of DNA strands to the physics of black holes. That thread initiated a research program of mine that’s yielded nine papers, garnered 19 collaborators, and spawned two experiments. Studying diverse subjects trained me to draw creative connections, which underlie much physics research.

I haven’t detailed all the benefits that a liberal-arts education can accrue to a physics career. For instance, the liberal arts enhance one’s communication skills, key to collaborating on research and to conveying one’s research. Without conveying one’s research adroitly, one likely won’t impact a field much. Also, a liberal-arts education can help one connect with researchers from across the globe on a personal level.3 Personal connections enhance science, which scientists—humans—undertake.

As I began building my research group, I sought advice from an MIT professor who’d attended MIT as an undergraduate. He advised me to seek students who have unusual backgrounds, including liberal-arts educations. Don’t get me wrong; I respect and cherish the colleagues and friends of mine who attended MIT, Caltech, and other tech schools as undergraduates. Still, I wouldn’t trade my German literature and economics. The liberal arts have enriched my physics research no less than they’ve enriched the rest of my life.

1A toolkit that overlaps partially with other disciplines’ toolkits, as explained in (3).

2I didn’t help much. When asked to guess the last concept in the triumvirate, I tried “debate.”

3I once met a Ukrainian physicist who referred to Ilya Muromets in a conversation. Ilya Muromets is a bogatyr, a knight featured in Slavic epics set in the Middle Ages. I happened to have taken a Slavic-folklore course the previous year. So I responded with a reference to Muromets’s pals, Dobrynya Nikitich and Alyosha Popovich. The physicist and I hit it off, and he taught me much about condensed matter over the following months.

Quantum steampunk is heading to bookstores!

I’m publishing a book! Quantum Steampunk: The Physics of Yesterday’s Tomorrow is hitting bookstores next spring, and you can preorder it now.

As Quantum Frontiers regulars know, steampunk is a genre of literature, art and film. Steampunkers fuse 19th-century settings (such as Victorian England, the Wild West, and Meiji Japan) with futuristic technologies (such as dirigibles, time machines, and automata). So does my field of research, a combination of thermodynamics, quantum physics, and information processing. 

Thermodynamics, the study of energy, developed during the Industrial Revolution. The field grew from practical concerns (How efficiently can engines pump water out of mines?) but wound up addressing fundamental questions (Why does time flow in only one direction?). Thermodynamics needs re-envisioning for 21st-century science, which spotlights quantum systems—electrons, protons, and other basic particles. Early thermodynamicists couldn’t even agree that atoms existed, let alone dream that quantum systems could process information in ways impossible for nonquantum systems. Over the past few decades, we’ve learned that quantum technologies can outperform their everyday counterparts in solving certain computational problems, in securing information, and in transmitting information. The study of quantum systems’ information-processing power forms a mathematical and conceptual toolkit, quantum information science. My colleagues and I leverage this toolkit to reconceptualize thermodynamics. As we combine a 19th-century framework (thermodynamics) with advanced technology (quantum information), I call our field quantum steampunk.

Glimpses of quantum steampunk have surfaced on this blog throughout the past eight years. The book is another animal, a 15-chapter closeup of the field. The book sets the stage with introductions to information processing, quantum physics, and thermodynamics. Then, we watch these three perspectives meld into one coherent whole. We tour the landscape of quantum thermodynamics—the different viewpoints and discoveries championed by different communities. These viewpoints, we find, offer a new lens onto the rest of science, including chemistry, black holes, and materials physics. Finally, we peer through a brass telescope to where quantum steampunk is headed next. Throughout the book, the science interleaves with anecdotes, history, and the story of one woman’s (my) journey into physics—and with snippets from a quantum-steampunk novel that I’ve dreamed up.

On this blog, different parts of my posts are intended for different audiences. Each post contains something for everyone, but not everyone will understand all of each post. In contrast, the book targets the general educated layperson. One of my editors majored in English, and another majored in biology, so the physics should come across clearly to everyone (and if it doesn’t, blame my editors). But the book will appeal to physicists, too. Reviewer Jay Lawrence, a professor emeritus of Dartmouth College’s physics department, wrote, “Presenting this vision [of quantum thermodynamics] in a manner accessible to laypeople discovering new interests, Quantum Steampunk will also appeal to specialists and aspiring specialists.” This book is for you.

Painting, by Robert Van Vranken, that plays a significant role in the book.

Strange to say, I began writing Quantum Steampunk under a year ago. I was surprised to receive an email from Tiffany Gasbarrini, a senior acquisitions editor at Johns Hopkins University Press, in April 2020. Tiffany had read the article I’d written about quantum steampunk for Scientific American. She wanted to expand the press’s offerings for the general public. Would I be interested in writing a book proposal? she asked.

Not having expected such an invitation, I poked around. The press’s roster included books that caught my eye, by thinkers I wanted to meet. From Wikipedia, I learned that Johns Hopkins University Press is “the oldest continuously running university press in the United States.” Senior colleagues of mine gave the thumbs-up. So I let my imagination run.

I developed a table of contents while ruminating on long walks, which I’d begun taking at the start of the pandemic. In late July, I submitted my book proposal. As the summer ended, I began writing the manuscript.

Writing the first draft—73,000 words—took about five months. The process didn’t disrupt life much. I’m used to writing regularly; I’ve written one blog post per month here since 2013, and I wrote two novels during and after college. I simply picked up my pace. At first, I wrote only on weekends. Starting in December 2020, I wrote 1,000 words per day. The process wasn’t easy, but it felt like a morning workout—healthy and productive. That productivity fed into my science, which fed back into the book. One of my current research projects grew from the book’s epilogue. A future project, I expect, will evolve from Chapter 5.

As soon as I finished draft one—last January—Tiffany and I hunted for an illustrator. We were fortunate to find Todd Cahill, a steampunk artist. He transformed the poor sketches that I’d made into works of art.

Steampunk illustration of a qubit, the basic unit of quantum information, by Todd Cahill

Early this spring, I edited the manuscript. That edit was to a stroll as the next edit was to the Boston Marathon. Editor Michael Zierler coached me through the marathon. He identified concepts that needed clarification, discrepancies between explanations, and analogies that had run away with me—as well as the visions and turns of phrase that delighted him, to balance the criticism. As Michael and I toiled, 17 of my colleagues were kind enough to provide feedback. They read sections about their areas of expertise, pointed out subtleties, and confirmed facts.

Soon after Michael and I crossed the finished line, copyeditor Susan Matheson took up the baton. She hunted for typos, standardized references, and more. Come June, I was editing again—approving and commenting on her draft. Simultaneously, Tiffany designed the cover, shown above, with more artists. The marketing team reached out, and I began planning this blog post. Scratch that—I’ve been dreaming about this blog post for almost a year. But I forced myself not to spill the beans here till I told the research group I’ve been building. I shared about the book with them two Thursdays ago, and I hope that book critics respond as they did.

Every time I’ve finished a draft, my husband and I have celebrated by ordering takeout sandwiches from our favorite restaurant. Three sandwich meals are down, and we have one to go.

Having dreamed about this blog post for a year, I’m thrilled to bits to share my book with you. It’s available for preordering, and I encourage you to support your local bookstore by purchasing through bookshop.org. The book is available also through Barnes & Noble, Amazon, Waterstones, and the other usual suspects. For press inquiries, or to request a review copy, contact Kathryn Marguy at kmarguy@jhu.edu.

Over the coming year, I’ll continue sharing about my journey into publishing—the blurbs we’ll garner for the book jacket, the first copies hot off the press, the reviews and interviews. I hope that you’ll don your duster coat and goggles (every steampunker wears goggles), hop into your steam-powered gyrocopter, and join me.

Cutting the quantum mustard

I had a relative to whom my parents referred, when I was little, as “that great-aunt of yours who walked into a glass door at your cousin’s birthday party.” I was a small child in a large family that mostly lived far away; little else distinguished this great-aunt from other relatives, in my experience. She’d intended to walk from my grandmother’s family room to the back patio. A glass door stood in the way, but she didn’t see it. So my great-aunt whammed into the glass; spent part of the party on the couch, nursing a nosebleed; and earned the epithet via which I identified her for years.

After growing up, I came to know this great-aunt as a kind, gentle woman who adored her family and was adored in return. After growing into a physicist, I came to appreciate her as one of my earliest instructors in necessary and sufficient conditions.

My great-aunt’s intended path satisfied one condition necessary for her to reach the patio: Nothing visible obstructed the path. But the path failed to satisfy a sufficient condition: The invisible obstruction—the glass door—had been neither slid nor swung open. Sufficient conditions, my great-aunt taught me, mustn’t be overlooked.

Her lesson underlies a paper I published this month, with coauthors from the Cambridge other than mine—Cambridge, England: David Arvidsson-Shukur and Jacob Chevalier Drori. The paper concerns, rather than pools and patios, quasiprobabilities, which I’ve blogged about many times [1,2,3,4,5,6,7]. Quasiprobabilities are quantum generalizations of probabilities. Probabilities describe everyday, classical phenomena, from Monopoly to March Madness to the weather in Massachusetts (and especially the weather in Massachusetts). Probabilities are real numbers (not dependent on the square-root of -1); they’re at least zero; and they compose in certain ways (the probability of sun or hail equals the probability of sun plus the probability of hail). Also, the probabilities that form a distribution, or a complete set, sum to one (if there’s a 70% chance of rain, there’s a 30% chance of no rain). 

In contrast, quasiprobabilities can be negative and nonreal. We call such values nonclassical, as they’re unavailable to the probabilities that describe classical phenomena. Quasiprobabilities represent quantum states: Imagine some clump of particles in a quantum state described by some quasiprobability distribution. We can imagine measuring the clump however we please. We can calculate the possible outcomes’ probabilities from the quasiprobability distribution.

Not from my grandmother’s house, although I wouldn’t mind if it were.

My favorite quasiprobability is an obscure fellow unbeknownst even to most quantum physicists: the Kirkwood-Dirac distribution. John Kirkwood defined it in 1933, and Paul Dirac defined it independently in 1945. Then, quantum physicists forgot about it for decades. But the quasiprobability has undergone a renaissance over the past few years: Experimentalists have measured it to infer particles’ quantum states in a new way. Also, colleagues and I have generalized the quasiprobability and discovered applications of the generalization across quantum physics, from quantum chaos to metrology (the study of how we can best measure things) to quantum thermodynamics to the foundations of quantum theory.

In some applications, nonclassical quasiprobabilities enable a system to achieve a quantum advantage—to usefully behave in a manner impossible for classical systems. Examples include metrology: Imagine wanting to measure a parameter that characterizes some piece of equipment. You’ll perform many trials of an experiment. In each trial, you’ll prepare a system (for instance, a photon) in some quantum state, send it through the equipment, and measure one or more observables of the system. Say that you follow the protocol described in this blog post. A Kirkwood-Dirac quasiprobability distribution describes the experiment.1 From each trial, you’ll obtain information about the unknown parameter. How much information can you obtain, on average over trials? Potentially more information if some quasiprobabilities are negative than if none are. The quasiprobabilities can be negative only if the state and observables fail to commute with each other. So noncommutation—a hallmark of quantum physics—underlies exceptional metrological results, as shown by Kirkwood-Dirac quasiprobabilities.

Exceptional results are useful, and we might aim to design experiments that achieve them. We can by designing experiments described by nonclassical Kirkwood-Dirac quasiprobabilities. When can the quasiprobabilities become nonclassical? Whenever the relevant quantum state and observables fail to commute, the quantum community used to believe. This belief turns out to mirror the expectation that one could access my grandmother’s back patio from the living room whenever no visible barriers obstructed the path. As a lack of visible barriers was necessary for patio access, noncommutation is necessary for Kirkwood-Dirac nonclassicality. But noncommutation doesn’t suffice, according to my paper with David and Jacob. We identified a sufficient condition, sliding back the metaphorical glass door on Kirkwood-Dirac nonclassicality. The condition depends on simple properties of the system, state, and observables. (Experts: Examples include the Hilbert space’s dimensionality.) We also quantified and upper-bounded the amount of nonclassicality that a Kirkwood-Dirac quasiprobability can contain.

From an engineering perspective, our results can inform the design of experiments intended to achieve certain quantum advantages. From a foundational perspective, the results help illuminate the sources of certain quantum advantages. To achieve certain advantages, noncommutation doesn’t cut the mustard—but we now know a condition that does.

For another take on our paper, check out this news article in Physics Today.  

1Really, a generalized Kirkwood-Dirac quasiprobability. But that phrase contains a horrendous number of syllables, so I’ll elide the “generalized.”

Peeking into the world of quantum intelligence

Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly.

An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future.
[Credit: Claudia Cheng]

We, as intelligent beings, receive, process, and store classical information. The information comes from vision, hearing, smell, and tactile sensing. The data is encoded as analog classical information through the electrical pulses sending through our nerve fibers. Our brain processes this information classically through neural circuits (at least that is our current understanding, but one should check out this blogpost). We then store this processed classical information in our hippocampus that allows us to retrieve it later to combine it with future information that we obtain. Finally, we use the stored classical information to make predictions about the future (imagine/predict the future outcomes if we perform certain action) and choose the action that would most likely be in our favor.

Such abilities have enabled us to make remarkable accomplishments: soaring in the sky by constructing accurate models of how air flows around objects, or building weak forms of intelligent beings capable of performing basic conversations and play different board games. Instead of receiving/processing/storing classical information, one could imagine some form of quantum intelligence that deals with quantum information instead of classical information. These quantum beings can receive quantum information through quantum sensors built up from tiny photons and atoms. They would then process this quantum information with quantum mechanical evolutions (such as quantum computers), and store the processed qubits in a quantum memory (protected with a surface code or toric code).

A caricature of human intelligence dating long before 1950, artificial intelligence that began in the 50’s, and the emergence of quantum intelligence.
[Credit: Claudia Cheng]

It is natural to wonder what a world of quantum intelligence would be like. While we have never encountered such a strange creature in the real world (yet), the mathematics of quantum mechanics, machine learning, and information theory allow us to peek into what such a fantastic world would be like. The physical world we live in is intrinsically quantum. So one may imagine that a quantum being is capable of making more powerful predictions than a classical being. Maybe he/she/they could better predict events that happened further away, such as tell us how a distant black hole was engulfing another? Or perhaps he/she/they could improve our lives, for example by presenting us with an entirely new approach for capturing energy from sunlight?

One may be skeptical about finding quantum intelligent beings in nature (and rightfully so). But it may not be so absurd to synthesize a weak form of quantum (artificial) intelligence in an experimental lab, or enhance our classical human intelligence with quantum devices to approximate a quantum-mechanical being. Many famous companies, like Google, IBM, Microsoft, and Amazon, as well as many academic labs and startups have been building better quantum machines/computers day by day. By combining the concepts of machine learning on classical computers with these quantum machines, the future of us interacting with some form of quantum (artificial) intelligence may not be so distant.

Before the day comes, could we peek into the world of quantum intelligence? And could one better understand how much more powerful they could be over classical intelligence?

A cartoon depiction of me (Left), Richard Kueng (Middle), and John Preskill (Right).
[Credit: Claudia Cheng]

In a recent publication [1], my advisor John Preskill, my good friend Richard Kueng, and I made some progress toward these questions. We consider a quantum mechanical world where classical beings could obtain classical information by measuring the world (performing POVM measurement). In contrast, quantum beings could retrieve quantum information through quantum sensors and store the data in a quantum memory. We study how much better quantum over classical beings could learn from the physical world to accurately predict the outcomes of unseen events (with the focus on the number of interactions with the physical world instead of computation time). We cast these problems in a rigorous mathematical framework and utilize high-dimensional probability and quantum information theory to understand their respective prediction power. Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis.

Formally, we consider the task of learning an unknown physical evolution described by a CPTP map \mathcal{E} that takes in n-qubit state and maps to m-qubit state. The classical model can select an arbitrary classical input to the CPTP map and measure the output state of the CPTP map with some POVM measurement. The quantum model can access the CPTP map coherently and obtain quantum data from each access, which is equivalent to composing multiple CPTP maps with quantum computations to learn about the CPTP map. The task is to predict a property of the output state \mathcal{E}(\lvert x \rangle\!\langle x \rvert), given by \mathrm{Tr}(O \mathcal{E}(\lvert x \rangle\!\langle x \rvert)), for a new classical input x \in \{0, 1\}^n. And the goal is to achieve the task while accessing \mathcal{E} as few times as possible (i.e., fewer interactions or experiments in the physical world). We denote the number of interactions needed by classical and quantum models as N_{\mathrm{C}}, N_{\mathrm{Q}}.

In general, quantum models could learn from fewer interactions with the physical world (or experiments in the physical world) than classical models. This is because coherent quantum information can facilitate better information synthesis with information obtained from previous experiments. Nevertheless, in [1], we show that there is a fundamental limit to how much more efficient quantum models can be. In order to achieve a prediction error

\mathbb{E}_{x \sim \mathcal{D}} |h(x) -  \mathrm{Tr}(O \mathcal{E}(\lvert x \rangle\!\langle x \rvert))| \leq \mathcal{O}(\epsilon),

where h(x) is the hypothesis learned from the classical/quantum model and \mathcal{D} is an arbitrary distribution over the input space \{0, 1\}^n, we found that the speed-up N_{\mathrm{C}} / N_{\mathrm{Q}} is upper bounded by m / \epsilon, where m > 0 is the number of qubits each experiment provides (the output number of qubits in the CPTP map \mathcal{E}), and \epsilon > 0 is the desired prediction error (smaller \epsilon means we want to predict more accurately).

In contrast, when we want to accurately predict all unseen events, we prove that quantum models could use exponentially fewer experiments than classical models. We give a construction for predicting properties of quantum systems showing that quantum models could substantially outperform classical models. These rigorous results show that quantum intelligence shines when we seek stronger prediction performance.

We have only scratched the surface of what is possible with quantum intelligence. As the future unfolds, I am hopeful that we will discover more that can be done only by quantum intelligence, through mathematical analysis, rigorous numerical studies, and physical experiments.

Further information:

  • A classical model that can be used to accurately predict properties of quantum systems is the classical shadow formalism [2] that we proposed a year ago. In many tasks, this model can be shown to be one of the strongest rivals that quantum models have to surpass.
  • Even if a quantum model only receives and stores classical data, the ability to process the data using a quantum-mechanical evolution can still be advantageous [3]. However, obtaining large advantage will be harder in this case as the computational power in data can slightly boost classical machines/intelligence [3].
  • Another nice paper by Dorit Aharonov, Jordan Cotler, and Xiao-Liang Qi [4] also proved advantages of quantum models over classical one in some classification tasks.

References:

[1] Huang, Hsin-Yuan, Richard Kueng, and John Preskill. “Information-Theoretic Bounds on Quantum Advantage in Machine Learning.” Physical Review Letters 126: 190505 (2021). https://doi.org/10.1103/PhysRevLett.126.190505

[2] Huang, Hsin-Yuan, Richard Kueng, and John Preskill. “Predicting many properties of a quantum system from very few measurements.” Nature Physics 16: 1050-1057 (2020). https://doi.org/10.1038/s41567-020-0932-7

[3] Huang, Hsin-Yuan, et al. “Power of data in quantum machine learning.” Nature communications 12.1 (2021): 1-9. https://doi.org/10.1038/s41467-021-22539-9

[4] Aharonov, Dorit, Jordan Cotler, and Xiao-Liang Qi. “Quantum Algorithmic Measurement.” arXiv preprint arXiv:2101.04634 (2021).

Learning about learning

The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing

Hard as I studied, my classmates enjoyed greater facility with the computer-science curriculum. They saw immediately how long an algorithm would run, while I hesitated and then computed the run time step by step. I felt behind. So I protested when my professor said, “You’re good at this.” 

I now see that we were focusing on different facets of learning. I rued my lack of intuition. My classmates had gained intuition by exploring computer science in high school, then slow-cooking their experiences on a mental back burner. Their long-term exposure to the material provided familiarity—the ability to recognize a new problem as belonging to a class they’d seen examples of. I was cooking course material in a mental microwave set on “high,” as a semester’s worth of material was crammed into ten weeks at my college.

My professor wasn’t measuring my intuition. He only saw that I knew how to compute an algorithm’s run time. I’d learned the material required of me—more than I realized, being distracted by what I hadn’t learned that difficult autumn.

We can learn a staggering amount when pushed far from our comfort zones—and not only we humans can. So can simple collections of particles.

Examples include a classical spin glass. A spin glass is a collection of particles that shares some properties with a magnet. Both a magnet and a spin glass consist of tiny mini-magnets called spins. Although I’ve blogged about quantum spins before, I’ll focus on classical spins here. We can imagine a classical spin as a little arrow that points upward or downward.  A bunch of spins can form a material. If the spins tend to point in the same direction, the material may be a magnet of the sort that’s sticking the faded photo of Fluffy to your fridge.

The spins may interact with each other, similarly to how electrons interact with each other. Not entirely similarly, though—electrons push each other away. In contrast, a spin may coax its neighbors into aligning or anti-aligning with it. Suppose that the interactions are random: Any given spin may force one neighbor into alignment, gently ask another neighbor to align, entreat a third neighbor to anti-align, and having nothing to say to neighbors four and five.

The spin glass can interact with the external world in two ways. First, we can stick the spins in a magnetic field, as by placing magnets above and below the glass. If aligned with the field, a spin has negative energy; and, if antialigned, positive energy. We can sculpt the field so that it varies across the spin glass. For instance, spin 1 can experience a strong upward-pointing field, while spin 2 experiences a weak downward-pointing field.

Second, say that the spins occupy a fixed-temperature environment, as I occupy a 74-degree-Fahrenheit living room. The spins can exchange heat with the environment. If releasing heat to the environment, a spin flips from having positive energy to having negative—from antialigning with the field to aligning.

Let’s perform an experiment on the spins. First, we design a magnetic field using random numbers. Whether the field points upward or downward at any given spin is random, as is the strength of the field experienced by each spin. We sculpt three of these random fields and call the trio a drive.

Let’s randomly select a field from the drive and apply it to the spin glass for a while; again, randomly select a field from the drive and apply it; and continue many times. The energy absorbed by the spins from the fields spikes, then declines.

Now, let’s create another drive of three random fields. We’ll randomly pick a field from this drive and apply it; again, randomly pick a field from this drive and apply it; and so on. Again, the energy absorbed by the spins spikes, then tails off.

Here comes the punchline. Let’s return to applying the initial fields. The energy absorbed by the glass will spike—but not as high as before. The glass responds differently to a familiar drive than to a new drive. The spin glass recognizes the original drive—has learned the first fields’ “fingerprint.” This learning happens when the fields push the glass far from equilibrium,1 as I learned when pushed during my mildly hellish autumn.

So spin glasses learn drives that push them far from equilibrium. So do many other simple, classical, many-particle systems: polymers, viscous liquids, crumpled sheets of Mylar, and more. Researchers have predicted such learning and observed it experimentally. 

Scientists have detected many-particle learning by measuring thermodynamic observables. Examples include the energy absorbed by the spin glass—what thermodynamicists call work. But thermodynamics developed during the 1800s, to describe equilibrium systems, not to study learning. 

One study of learning—the study of machine learning—has boomed over the past two decades. As described by the MIT Technology Review, “[m]achine-learning algorithms use statistics to find patterns in massive amounts of data.” Users don’t tell the algorithms how to find those patterns.

xkcd.com/1838

It seems natural and fitting to use machine learning to learn about the learning by many-particle systems. That’s what I did with collaborators from the group of Jeremy England, a GlaxoSmithKline physicist who studies complex behaviors of many particle systems. Weishun Zhong, Jacob Gold, Sarah Marzen, Jeremy, and I published our paper last month. 

Using machine learning, we detected and measured many-particle learning more reliably and precisely than thermodynamic measures seem able to. Our technique works on multiple facets of learning, analogous to the intuition and the computational ability I encountered in my computer-science course. We illustrated our technique on a spin glass, but one can apply our approach to other systems, too. I’m exploring such applications with collaborators at the University of Maryland.

The project pushed me far from my equilibrium: I’d never worked with machine learning or many-body learning. But it’s amazing, what we can learn when pushed far from equilibrium. I first encountered this insight sophomore fall of college—and now, we can quantify it better than ever.

1Equilibrium is a quiet, restful state in which the glass’s large-scale properties change little. No net flow of anything—such as heat or particles—enter or leave the system.