The quantum steampunker by Massachusetts Bay

Every spring, a portal opens between Waltham, Massachusetts and another universe. 

The other universe has a Watch City dual to Waltham, known for its watch factories. The cities throw a festival to which explorers, inventors, and tourists flock. Top hats, goggles, leather vests, bustles, and lace-up boots dot the crowds. You can find pet octopodes, human-machine hybrids, and devices for bending space and time. Steam powers everything.

Watch City

Watch City Steampunk Festival

So I learned thanks to Maxim Olshanyi, a professor of physics at the University of Massachusetts Boston. He hosted my colloquium, “Quantum steampunk: Quantum information meets thermodynamics,” earlier this month. Maxim, I discovered, has more steampunk experience than I. He digs up century-old designs for radios, builds the radios, and improves upon the designs. He exhibits his creations at the Watch City Steampunk Festival.

Maxim photo

Maxim Olshanyi

I never would have guessed that Maxim moonlights with steampunkers. But his hobby makes sense: Maxim has transformed our understanding of quantum integrability.

Integrability is to thermalization as Watch City is to Waltham. A bowl of baked beans thermalizes when taken outside in Boston in October: Heat dissipates into the air. After half-an-hour, large-scale properties bear little imprint of their initial conditions: The beans could have begun at 112ºF or 99º or 120º. Either way, the beans have cooled.

Integrable systems avoid thermalizing; more of their late-time properties reflect early times. Why? We can understand through an example, an integrable system whose particles don’t interact with each other (whose particles are noninteracting fermions). The dynamics conserve the particles’ momenta. Consider growing the system by adding particles. The number of conserved quantities grows as the system size. The conserved quantities retain memories of the initial conditions.

Imagine preparing an integrable system, analogously to preparing a bowl of baked beans, and letting it sit for a long time. Will the system equilibrate, or settle down to, a state predictable with a simple rule? We might expect not. Obeying the same simple rule would cause different integrable systems to come to resemble each other. Integrable systems seem unlikely to homogenize, since each system retains much information about its initial conditions.

Boston baked beans

Maxim and collaborators exploded this expectation. Integrable systems do relax to simple equilibrium states, which the physicists called the generalized Gibbs ensemble (GGE). Josiah Willard Gibbs cofounded statistical mechanics during the 1800s. He predicted the state to which nonintegrable systems, like baked beans in autumnal Boston, equilibrate. Gibbs’s theory governs classical systems, like baked beans, as does the GGE theory. But also quantum systems equilibrate to the GGE, and Gibbs’s conclusions translate into quantum theory with few adjustments. So I’ll explain in quantum terms.

Consider quantum baked beans that exchange heat with a temperature-T environment. Let \hat{H} denote the system’s Hamiltonian, which basically represents the beans’ energy. The beans equilibrate to a quantum Gibbs state, e^{ - \hat{H} / ( k_{\rm B} T ) } / Z. The k_{\rm B} denotes Boltzmann’s constant, a fundamental constant of nature. The partition function Z enables the quantum state to obey probability theory (normalizes the state).

Maxim and friends modeled their generalized Gibbs ensemble on the Gibbs state. Let \hat{I}_m denote a quantum integrable system’s m^{\rm th} conserved quantity. This system equilibrates to e^{ - \sum_m \lambda_m \hat{I}_m } / Z_{\rm GGE}. The Z_{\rm GGE} normalizes the state. The intensive parameters \lambda_m’s serve analogously to temperature and depend on the conserved quantities’ values. Maxim and friends predicted this state using information theory formalized by Ed Jaynes. Inventing the GGE, they unlocked a slew of predictions about integrable quantum systems. 

Olchanyi__radioboard_comp_2015_picture

A radio built by Maxim. According to him, “The invention was to replace a diode with a diode bridge, in a crystal radio, thus gaining a factor of two in the output power.”

I define quantum steampunk as the intersection of quantum theory, especially quantum information theory, with thermodynamics, and the application of this intersection across science. Maxim has used information theory to cofound a branch of quantum statistical mechanics. Little wonder that he exhibits homemade radios at the Watch City Steampunk Festival. He also holds a license to drive steam engines and used to have my postdoc position. I appreciate having older cousins to look up to. Here’s hoping that I become half the quantum steampunker that I found by Massachusetts Bay.

With thanks to Maxim and the rest of the University of Massachusetts Boston Department of Physics for their hospitality.

The next Watch City Steampunk Festival takes place on May 9, 2020. Contact me if you’d attend a quantum-steampunk meetup!

Sultana: The Girl Who Refused To Stop Learning

Sultana at Caltech, Pasadena, CA

Caltech attracts some truly unique individuals from all across the globe with a passion for figuring things out. But there was one young woman on campus this past summer whose journey towards scientific research was uniquely inspiring.

Sultana spent the summer at Caltech in the SURF program, working on next generation quantum error correction codes under the supervision of Dr. John Preskill. As she wrapped up her summer project, returning to her “normal” undergraduate education in Arizona, I had the honor of helping her document her remarkable journey. This is her story:

Afghanistan

My name is Sultana. I was born in Afghanistan. For years I was discouraged and outright prevented from going to school by the war. It was not safe for me because of the active war and violence in the region, even including suicide bombings. Society was still recovering from the decades long civil war, the persistent influence of a dethroned, theocratically regressive regime and the current non-functioning government. These forces combined to make for a very insecure environment for a woman. It was tacitly accepted that the only place safe for a woman was to remain at home and stay quiet. Another consequence of these circumstances was that the teachers at local schools were all male and encouraged the girls to not come to school and study. What was the point if at the end of the day a woman’s destiny was to stay at home and cook? 

For years, I would be up every day at 8am and every waking hour was devoted to housework and preparing the house to host guests, typically older women and my grandmother’s friends. I was destined to be a homemaker and mother. My life had no meaning outside of those roles.

My brothers would come home from school, excited about mathematics and other subjects. For them, it seemed like life was full of infinite possibilities. Meanwhile I had been confined to be behind the insurmountable walls of my family’s compound. All the possibilities for my life had been collapsed, limited to a single identity and purpose.

At fourteen I had had enough. I needed to find a way out of the mindless routine and depressing destiny. And more specifically, I wanted to understand how complex, and clearly powerful, human social systems, such as politics, economics and culture, combined to create overtly negative outcomes like imbalance and oppression. I made the decision to wake up two hours early every day to learn English, before taking on the day’s expected duties.

My grandfather had a saying, “If you know English, then you don’t have to worry about where the food is going to come from.”

He taught himself English and eventually became a professor of literature and humanities. He had even encouraged his five daughters to pursue advanced education. My aunts became medical doctors and chemists (one an engineer, another a teacher). My mother became a lecturer at a university, a profession she would be forced to leave when the Mujaheddin came to power.

I started by studying newspapers and any book I could get my hands on. My hunger for knowledge proved insatiable.

When my father got the internet, the floodgates of information opened. I found and took online courses through sites like Khan Academy and, later, Coursera.

I was intrigued by discussions between my brothers on mathematics. Countless pages of equations and calculations could propagate from a single, simple question; just like how a complex and towering tree can emerge from a single seed.

Khan Academy provided a superbly structured approach to learning mathematics from scratch. Most importantly, mathematics did not rely on a mastery of English as a prerequisite.

Over the next few years I consumed lesson after lesson, expanding my coursework into physics. I would supplement this unorthodox yet structured education with a more self-directed investigation into philosophy through books like Kant’s Critique of Pure Reason. While math and physics helped me develop confidence and ability, ultimately, I was still driven by trying to understand the complexities of human behavior and social systems.

Sultana & EmilyEmily from Iowa

To further develop my hold on English I enrolled in a Skype-based student exchange program and made a critical friend in Emily from Iowa. After only a few conversations, Emily suggested that my English was so good that I should consider taking the SAT and start applying for schools. She soon became a kind of college counselor for me.

Even though my education was stonewalled by an increasingly repressive socio-political establishment, I had the full support of my family. There were no SAT testing locations in Afghanistan. So when it was clear to my family I had the potential to get a college education, my uncle took me across the border into Pakistan, to take the SAT. However, a passport from Afghanistan was required to take the test and, when it was finally granted, it had to be smuggled across the border. Considering that I had no formal education and little time to study for the SAT, I earned a surprisingly competitive score on the exam.

My confidence soared and I convinced my family to make the long trek to the American embassy and apply for a student visa. I was denied in less than sixty seconds! They thought I would end up not studying and becoming an economic burden. I was crushed. And my immaturely formed vision of the world was clearly more idealized than the reality that presented itself and slammed its door in my face. I was even more confused by how the world worked and I immediately became invested in understanding politics.

The New York Times

Emily was constantly working in the background on my behalf, and on the other side of the world, trying to get the word out about my struggle. This became her life’s project, to somehow will me into a position to attend a university. New York Times writer Nicholas Kristoff heard about my story and we conducted an interview over Skype. The story was published in the summer of 2016.

The New York Times opinion piece was published in June. Ironically, I didn’t have much say or influence on the opinion-editorial piece. I felt that the piece was overly provocative.

Even now, because family members still live under the threat of violence, I will not allow myself to be photographed. Suffice to say, I never wanted to stir up trouble, or call attention to myself. Even so, the net results of that article are overwhelmingly positive. I was even offered a scholarship to attend Arizona State University; that was, if I could secure a visa.

I was pessimistic. I had been rejected twice already by what should have been the most logical and straightforward path towards formal education in America. How was this special asylum plea going to result in anything different? But Nicholas Kristoff was absolutely certain I would get it. He gave my case to an immigration lawyer with a relationship to the New York Times. In just a month and a half I was awarded humanitarian parole. This came with some surprising constraints, including having to fly to the U.S. within ten days and a limit of four months to stay there while applying for asylum. As quickly as events were unfolding, I didn’t even hesitate.

As I was approaching America, I realized that over 5,000 miles of water would now separate me from the most influential forces in my life. The last of these flights took me deep into the center of America, about a third of the way around the planet.

The clock was ticking on my time in America – at some point, factors and decisions outside of my control would deign that I was safe to go back to Afghanistan – so I exhausted every opportunity to obtain knowledge while I was isolated from the forces that would keep me from formal education. I petitioned for an earlier than expected winter enrollment at Arizona State University. In the meantime, I continued my self-education through edX classes (coursework from MIT made available online), as well as with Khan Academy and Coursera.

Camelback Mountain overlooking Phoenix, AZ

Phoenix

The answer came back from Arizona State University. They had granted me enrollment for the winter quarter. In December of 2016, I flew to the next state in my journey for intellectual independence and began my first full year of formal education at the largest university in America. Mercifully, my tenure in Phoenix began in the cool winter months. In fact, the climate was very similar to what I knew in Afghanistan.

However, as summer approached, I began to have a much different experience. This was the first time I was living on my own. It took me a while to be accustomed to that. I would generally stay in my room and study, even avoiding classes. The intensifying heat of the Arizona sun ensured that I would stay safely and comfortably encased inside. And I was actually doing okay. At first.

Happy as I was to finally be a part of formal education, it was in direct conflict with the way in which I had trained myself to learn. The rebellious spirit which helped me defy the cultural norms and risk harm to myself and my family, the same fire that I had to continuously stoke for years on my own, also made me rebel against the system that actively wanted me to learn. I constantly felt that I had better approaches to absorb the material and actively ignored the homework assignments. Naturally, my grades suffered and I was forced to make a difficult internal adjustment. I also benefited from advice from Emily, as well as a cousin who was pursuing education in Canada.

As I gritted my teeth and made my best attempts to adopt the relatively rigid structures of formal education, I began to feel more and more isolated. I found myself staying in my room day after day, focused simply on studying. But for what purpose? I was aimless. A machine of insatiable learning, but without any specific direction to guide my curiosity. I did not know it at the time, but I was desperate for something to motivate me.

The ripples from the New York Times piece were still reverberating and Sultana was contacted by author Betsy Devine. Betsy was a writer who had written a couple of books with notable scientists. Betsy was particularly interested in introducing Sultana to her husband, Nobel prize winner in physics, Frank Wilczek.

The first time I met Frank Wilczek was at lunch with with him and his wife. Wilczek enjoys hiking in the mountains overlooking surrounding Phoenix and Betsy suggested that I join Frank on an early morning hike. A hike. With Frank Wilczek. This was someone whose book, A Beautiful Question: Finding Nature’s Deep Design, I had read while in Afghanistan. To say that I was nervous is an understatement, but thankfully we fell into an easy flow of conversation. After going over my background and interests he asked me if I was interested in physics. I told him that I was, but I was principally interested in concepts that could be applied very generally, broadly – so that I could better understand the underpinnings of how society functions.

He told me that I should pursue quantum physics. And more specifically, he got me very excited about the prospects of quantum computers. It felt like I was placed at the start of a whole new journey, but I was walking on clouds. I was filled with a confidence that could only be generated by finding oneself comfortable in casual conversation with a Nobel laureate.

Immediately after the hike I went and collected all of the relevant works Wilczek had suggested, including Dirac’s “The Principles of Quantum Mechanics.”

Reborn

With a new sense of purpose, I immersed myself in the formal coursework, as well as my own, self-directed exploration of quantum physics. My drive was rewarded with all A’s in the fall semester of my sophomore year.

That same winter Nicholas Kristoff had published his annual New York Times opinion review of the previous year titled, “Why 2017 Was the Best Year in Human History.” I was mentioned briefly.

It was the start of the second semester of my sophomore year, and I was starting to feel a desire to explore applied physics. I was enrolled in a graduate-level seminar class in quantum theory that spring. One of the lecturers for the class was a young female professor who was interested in entropy, and more importantly, how we can access seemingly lost information. In other words, she wanted access to the unknown.

To that end, she was interested in gauge/gravity duality models like the one meant to explain the black hole “firewall” paradox, or the Anti-de Sitter space/conformal field theory (AdS/CFT) correspondence that uses a model of the universe where space-time has negative, hyperbolic curvature.

The geometry of 5D space-time in AdS space resembles that of an M.C.Escher drawing, where fish wedge themselves together, end-to-end, tighter and tighter as we move away from the origin. These connections between fish are consistent, radiating in an identical pattern, infinitely approaching the edge.

Unbeknownst to me, a friend of that young professor had read the Times opinion article. The article not only mentioned that I had been teaching myself string theory, but also that I was enrolled at Arizona State University and taking graduate level courses. She asked the young professor if she would be interested in meeting me.

The young professor invited me to her office, she told me about how black holes were basically a massive manifestation of entropy, and the best laboratory by which to learn the true nature of information loss, and how it might be reversed. We discussed the possibility of working on a research paper to help her codify the quantum component for her holographic duality models.

I immediately agreed. If there was anything in physics as difficult as understanding human social, religious and political dynamics, it was probably understanding the fundamental nature of space and time. Because the AdS/CFT model of spacetime was negatively curved, we could employ something called holographic quantum error correction to create a framework by which the information of a bulk entity (like a black hole) can be preserved at its boundary, even with some of its physical components (particles) becoming corrupted, or lost.

I spent the year wrestling with, and developing, quantum error correcting codes for a very specific kind of black hole. I learned that information has a way of protecting itself from decay through correlations. For instance, a single logical quantum bit (or “qubit”) of information can be represented, or preserved, by five stand-in, or physical, qubits. At a black hole’s event horizon, where entangled particles are pulled apart, information loss can be prevented as long as less than three-out-of-five of the representative physical qubits are lost to the black hole interior. The original quantum information can be recalled by using a quantum code to reverse this “error”.

By the end of my sophomore year I was nominated to represent Arizona State University at an inaugural event supporting undergraduate women in science. The purpose of the event was to help prepare promising women in physics for graduate school applications, as well as provide information on life as a graduate student. The event, called FUTURE of Physics, was to be held at Caltech.

I mentioned the nomination to Frank Wilczek and he excitedly told me that I must use the opportunity to meet Dr. John Preskill, who was at the forefront of quantum computing and quantum error correction. He reminded me that the best advice he could give anyone was to “find interesting minds and bother them.”

FUTURE 2018 at Caltech, Pasadena, CA

Pasadena

I spent two exciting days at Caltech with 32 other young women from all over the country on November 1st and 2nd of 2018. I was fortunate to meet John Preskill. And of course I introduced myself like any normal human being would, by asking him about the Shor factoring algorithm. I even got to attend a Wednesday group meeting with all of the current faculty and postdocs at IQIM. When I returned to ASU I sent an email to Dr. Preskill inquiring about potentially joining a short research project with his team.

I was extremely relieved when months later I received a response and an invitation to apply for the Summer Undergraduate Research Fellowship (SURF) at Caltech. Because Dr. Preskill’s recent work has been at the forefront of quantum error correction for quantum computing it was relatively straightforward to come up with a research proposal that aligned with the interests of my research adviser at ASU.

One of the major obstacles to efficient and widespread proliferation of quantum computers is the corruption of qubits, expensively held in very delicate low-energy states, by environmental interference and noise. People simply don’t, and should not, have confidence in practical, everyday use of quantum computers without reliable quantum error correction. The proposal was to create a proof that, if you’re starting with five physical qubits (representing a single logical qubit) and lose two of those qubits due to error, you can work backwards to recreate the original five qubits, and recover the lost logical qubit in the context of holographic error correcting codes. My application was accepted, and I made my way to Pasadena at the beginning of this summer.

The temperate climate, mountains and lush neighborhoods were a welcome change, especially with the onslaught of relentless heat that was about to envelope Phoenix.

Even at a campus as small as Caltech I felt like the smallest, most insignificant fish in a tiny, albeit prestigious, pond. But soon I was being connected to many like-minded, heavily motivated mathematicians and physicists, from all walks of life and from every corner of the Earth. Seasoned, young post-docs, like Grant Salton and Victor Albert introduced me to HaPPY tensors. HaPPY tensors are a holographic tensor network model developed by Dr. Preskill and colleagues meant to represent a toy model of AdS/CFT. Under this highly accessible and world-class mentorship, and with essentially unlimited resources, I wrestled with HaPPY tensors all summer and successfully discovered a decoder that could recover five qubits from three.

Example of tensor network causal and entanglement wedge reconstructions. From a blog post by Beni Yoshida on March 27th, 2015 on Quantum Frontiers.

This was the ultimate confidence booster. All the years of doubting myself and my ability, due to educating myself in a vacuum, lacking the critical feedback provided by real mentors, all disappeared.

Tomorrow

Now returning to ASU to finish my undergraduate education, I find myself still thinking about what’s next. I still have plans to expand my proof, extending beyond five qubits, to a continuous variable representation, and writing a general algorithm for an arbitrary N layer tensor-network construction. My mentors at Caltech have graciously extended their support to this ongoing work. And I now dream to become a professor of physics at an elite institution where I can continue to pursue the answers to life’s most confusing problems.

My days left in America are not up to me. I am applying for permanent amnesty so I can continue to pursue my academic dreams, and to take a crack at some of the most difficult problems facing humanity, like accelerating the progress towards quantum computing. I know I can’t pursue those goals back in Afghanistan. At least, not yet. Back there, women like myself are expected to stay at home, prepare food and clean the house for everybody else.

Little do they know how terrible I am at housework – and how much I love math.

Yes, seasoned scientists do extraordinary science.

Imagine that you earned tenure and your field’s acclaim decades ago. Perhaps you received a Nobel Prize. Perhaps you’re directing an institute for science that you helped invent. Do you still do science? Does mentoring youngsters, advising the government, raising funds, disentangling logistics, presenting keynote addresses at conferences, chairing committees, and hosting visitors dominate the time you dedicate to science? Or do you dabble, attend seminars, and read, following progress without spearheading it?

People have asked whether my colleagues do science when weighed down with laurels. The end of August illustrates my answer.

At the end of August, I participated in the eighth Conference on Quantum Information and Quantum Control (CQIQC) at Toronto’s Fields Institute. CQIQC bestows laurels called “the John Stewart Bell Prize” on quantum-information scientists. John Stewart Bell revolutionized our understanding of entanglement, strong correlations that quantum particles can share and that power quantum computing. Aephraim Steinberg, vice-chair of the selection committee, bestowed this year’s award. The award, he emphasized, recognizes achievements accrued during the past six years. This year’s co-winners have been leading quantum information theory for decades. But the past six years earned the winners their prize.

Fields

Peter Zoller co-helms IQOQI in Innsbruck. (You can probably guess what the acronym stands for. Hint: The name contains “Quantum” and “Institute.”) Ignacio Cirac is a director of the Max Planck Institute of Quantum Optics near Munich. Both winners presented recent work about quantum many-body physics at the conference. You can watch videos of their talks here.

Peter discussed how a lab in Austria and a lab across the world can check whether they’ve prepared the same quantum state. One lab might have trapped ions, while the other has ultracold atoms. The experimentalists might not know which states they’ve prepared, and the experimentalists might have prepared the states at different times. Create multiple copies of the states, Peter recommended, measure the copies randomly, and play mathematical tricks to calculate correlations.

Ignacio expounded upon how to simulate particle physics on a quantum computer formed from ultracold atoms trapped by lasers. For expert readers: Simulate matter fields with fermionic atoms and gauge fields with bosonic atoms. Give the optical lattice the field theory’s symmetries. Translate the field theory’s Lagrangian into Hamiltonian language using Kogut and Susskind’s prescription. 

Laurels 1

Even before August, I’d collected an arsenal of seasoned scientists who continue to revolutionize their fields. Frank Wilczek shared a physics Nobel Prize for theory undertaken during the 1970s. He and colleagues helped explain matter’s stability: They clarified how close-together quarks (subatomic particles) fail to attract each other, though quarks draw together when far apart. Why stop after cofounding one subfield of physics? Frank spawned another in 2012. He proposed the concept of a time crystal, which is like table salt, except extended across time instead of across space. Experimentalists realized a variation on Frank’s prediction in 2018, and time crystals have exploded across the scientific literature.1

Rudy Marcus is 96 years old. He received a chemistry Nobel Prize, for elucidating how electrons hop between molecules during reactions, in 1992. I took a nonequilibrium-statistical-mechanics course from Rudy four years ago. Ever since, whenever I’ve seen him, he’s asked for the news in quantum information theory. Rudy’s research group operates at Caltech, and you won’t find “Emeritus” in the title on his webpage.

My PhD supervisor, John Preskill, received tenure at Caltech for particle-physics research performed before 1990. You might expect the rest of his career to form an afterthought. But he helped establish quantum computing, starting in the mid-1990s. During the past few years, he co-midwifed the subfield of holographic quantum information theory, which concerns black holes, chaos, and the unification of quantum theory with general relativity. Watching a subfield emerge during my PhD left a mark like a tree on a bicyclist (or would have, if such a mark could uplift instead of injure). John hasn’t helped create subfields only by garnering resources and encouraging youngsters. Several papers by John and collaborators—about topological quantum matter, black holes, quantum error correction, and more—have transformed swaths of physics during the past 15 years. Nor does John stamp his name on many papers: Most publications by members of his group don’t list him as a coauthor.

Laurels 2

Do my colleagues do science after laurels pile up on them? The answer sounds to me, in many cases, more like a roar than like a “yes.” Much science done by senior scientists inspires no less than the science that established them. Beyond their results, their enthusiasm inspires. Never mind receiving a Bell Prize. Here’s to working toward deserving a Bell Prize every six years.

 

With thanks to the Fields Institute, the University of Toronto, Daniel F. V. James, Aephraim Steinberg, and the rest of the conference committee for their invitation and hospitality.

You can find videos of all the conference’s talks here. My talk is shown here

1To scientists, I recommend this Physics Today perspective on time crystals. Few articles have awed and inspired me during the past year as much as this review did. 

Quantum conflict resolution

If only my coauthors and I had quarreled.

I was working with Tony Bartolotta, a PhD student in theoretical physics at Caltech, and Jason Pollack, a postdoc in cosmology at the University of British Columbia. They acted as the souls of consideration. We missed out on dozens of opportunities to bicker—about the paper’s focus, who undertook which tasks, which journal to submit to, and more. Bickering would have spiced up the story behind our paper, because the paper concerns disagreement.

Quantum observables can disagree. Observables are measurable properties, such as position and momentum. Suppose that you’ve measured a quantum particle’s position and obtained an outcome x. If you measure the position immediately afterward, you’ll obtain x again. Suppose that, instead of measuring the position again, you measure the momentum. All the possible outcomes have equal probabilities of obtaining. You can’t predict the outcome.

The particle’s position can have a well-defined value, or the momentum can have a well-defined value, but the observables can’t have well-defined values simultaneously. Furthermore, if you measure the position, you randomize the outcome of a momentum measurement. Position and momentum disagree.

Tug-of-war

How should we quantify the disagreement of two quantum observables, \hat{A} and \hat{B}? The question splits physicists into two camps. Pure quantum information (QI) theorists use uncertainty relations, whereas condensed-matter and high-energy physicists prefer out-of-time-ordered correlators. Let’s meet the camps in turn.

Heisenberg intuited an uncertainty relation that Robertson formalized during the 1920s,

\Delta \hat{A} \, \Delta \hat{B} \geq \frac{1}{i \hbar} \langle [\hat{A}, \hat{B}] \rangle.

Imagine preparing a quantum state | \psi \rangle and measuring \hat{A}, then repeating this protocol in many trials. Each trial has some probability p_a of yielding the outcome a. Different trials will yield different a’s. We quantify the spread in a values with the standard deviation \Delta \hat{A} = \sqrt{ \langle \psi | \hat{A}^2 | \psi \rangle - \langle \psi | \hat{A} | \psi \rangle^2 }. We define \Delta \hat{B} analogously. \hbar denotes Planck’s constant, a number that characterizes our universe as the electron’s mass does. 

[\hat{A}, \hat{B}] denotes the observables’ commutator. The numbers that we use in daily life commute: 7 \times 5 = 5 \times 7. Quantum numbers, or operators, represent \hat{A} and \hat{B}. Operators don’t necessarily commute. The commutator [\hat{A}, \hat{B}] = \hat{A} \hat{B} - \hat{B} \hat{A} represents how little \hat{A} and \hat{B} resemble 7 and 5. 

Robertson’s uncertainty relation means, “If you can predict an \hat{A} measurement’s outcome precisely, you can’t predict a \hat{B} measurement’s outcome precisely, and vice versa. The uncertainties must multiply to at least some number. The number depends on how much \hat{A} fails to commute with \hat{B}.” The higher an uncertainty bound (the greater the inequality’s right-hand side), the more the operators disagree.

fistfight-cloud

Heisenberg and Robertson explored operator disagreement during the 1920s. They wouldn’t have seen eye to eye with today’s QI theorists. For instance, QI theorists consider how we can apply quantum phenomena, such as operator disagreement, to information processing. Information processing includes cryptography. Quantum cryptography benefits from operator disagreement: An eavesdropper must observe, or measure, a message. The eavesdropper’s measurement of one observable can “disturb” a disagreeing observable. The message’s sender and intended recipient can detect the disturbance and so detect the eavesdropper.

How efficiently can one perform an information-processing task? The answer usually depends on an entropy H, a property of quantum states and of probability distributions. Uncertainty relations cry out for recasting in terms of entropies. So QI theorists have devised entropic uncertainty relations, such as

H (\hat{A}) + H( \hat{B} ) \geq - \log c. \qquad (^*)

The entropy H( \hat{A} ) quantifies the difficulty of predicting the outcome a of an \hat{A} measurement. H( \hat{B} ) is defined analogously. c is called the overlap. It quantifies your ability to predict what happens if you prepare your system with a well-defined \hat{A} value, then measure \hat{B}. For further analysis, check out this paper. Entropic uncertainty relations have blossomed within QI theory over the past few years. 

Blossom

Pure QI theorists, we’ve seen, quantify operator disagreement with entropic uncertainty relations. Physicists at the intersection of condensed matter and high-energy physics prefer out-of-time-ordered correlators (OTOCs). I’ve blogged about OTOCs so many times, Quantum Frontiers regulars will be able to guess the next two paragraphs. 

Consider a quantum many-body system, such as a chain of qubits. Imagine poking one end of the system, such as by flipping the first qubit upside-down. Let the operator \hat{W} represent the poke. Suppose that the system evolves chaotically for a time t afterward, the qubits interacting. Information about the poke spreads through many-body entanglement, or scrambles.

Spin chain

Imagine measuring an observable \hat{V} of a few qubits far from the \hat{W} qubits. A little information about \hat{W} migrates into the \hat{V} qubits. But measuring \hat{V} reveals almost nothing about \hat{W}, because most of the information about \hat{W} has spread across the system. \hat{V} disagrees with \hat{W}, in a sense. Actually, \hat{V} disagrees with \hat{W}(t). The (t) represents the time evolution.

The OTOC’s smallness reflects how much \hat{W}(t) disagrees with \hat{V} at any instant t. At early times t \gtrsim 0, the operators agree, and the OTOC \approx 1. At late times, the operators disagree loads, and the OTOC \approx 0.

Dove

Different camps of physicists, we’ve seen, quantify operator disagreement with different measures: Today’s pure QI theorists use entropic uncertainty relations. Condensed-matter and high-energy physicists use OTOCs. Trust physicists to disagree about what “quantum operator disagreement” means.

I want peace on Earth. I conjectured, in 2016 or so, that one could reconcile the two notions of quantum operator disagreement. One must be able to prove an entropic uncertainty relation for scrambling, wouldn’t you think?

You might try substituting \hat{W}(t) for the \hat{A} in Ineq. {(^*)}, and \hat{V} for the \hat{B}. You’d expect the uncertainty bound to tighten—the inequality’s right-hand side to grow—when the system scrambles. Scrambling—the condensed-matter and high-energy-physics notion of disagreement—would coincide with a high uncertainty bound—the pure-QI-theory notion of disagreement. The two notions of operator disagreement would agree. But the bound I’ve described doesn’t reflect scrambling. Nor do similar bounds that I tried constructing. I banged my head against the problem for about a year.

Handshake

The sky brightened when Jason and Tony developed an interest in the conjecture. Their energy and conversation enabled us to prove an entropic uncertainty relation for scrambling, published this month.1 We tested the relation in computer simulations of a qubit chain. Our bound tightens when the system scrambles, as expected: The uncertainty relation reflects the same operator disagreement as the OTOC. We reconciled two notions of quantum operator disagreement.

As Quantum Frontiers regulars will anticipate, our uncertainty relation involves weak measurements and quasiprobability distributions: I’ve been studying their roles in scrambling over the past three years, with colleagues for whose collaborations I have the utmost gratitude. I’m grateful to have collaborated with Tony and Jason. Harmony helps when you’re tackling (quantum operator) disagreement—even if squabbling would spice up your paper’s backstory.

 

1Thanks to Communications Physics for publishing the paper. For pedagogical formatting, read the arXiv version. 

What distinguishes quantum thermodynamics from quantum statistical mechanics?

Yoram Alhassid asked the question at the end of my Yale Quantum Institute colloquium last February. I knew two facts about Yoram: (1) He belongs to Yale’s theoretical-physics faculty. (2) His PhD thesis’s title—“On the Information Theoretic Approach to Nuclear Reactions”—ranks among my three favorites.1 

Over the past few months, I’ve grown to know Yoram better. He had reason to ask about quantum statistical mechanics, because his research stands up to its ears in the field. If forced to synopsize quantum statistical mechanics in five words, I’d say, “study of many-particle quantum systems.” Examples include gases of ultracold atoms. If given another five words, I’d add, “Calculate and use partition functions.” A partition function is a measure of the number of states, or configurations, accessible to the system. Calculate a system’s partition function, and you can calculate the system’s average energy, the average number of particles in the system, how the system responds to magnetic fields, etc.

Line in the sand

My colloquium concerned quantum thermodynamics, which I’ve blogged about many times. So I should have been able to distinguish quantum thermodynamics from its neighbors. But the answer I gave Yoram didn’t satisfy me. I mulled over the exchange for a few weeks, then emailed Yoram a 502-word essay. The exercise grew my appreciation for the question and my understanding of my field. 

An adaptation of the email appears below. The adaptation should suit readers who’ve majored in physics, but don’t worry if you haven’t. Bits of what distinguishes quantum thermodynamics from quantum statistical mechanics should come across to everyone—as should, I hope, the value of question-and-answer sessions:

One distinction is a return to the operational approach of 19th-century thermodynamics. Thermodynamicists such as Sadi Carnot wanted to know how effectively engines could operate. Their practical questions led to fundamental insights, such as the Carnot bound on an engine’s efficiency. Similarly, quantum thermodynamicists often ask, “How can this state serve as a resource in thermodynamic tasks?” This approach helps us identify what distinguishes quantum theory from classical mechanics.

For example, quantum thermodynamicists found an advantage in charging batteries via nonlocal operations. Another example is the “MBL-mobile” that I designed with collaborators. Many-body localization (MBL), we found, can enhance an engine’s reliability and scalability. 

Asking, “How can this state serve as a resource?” leads quantum thermodynamicists to design quantum engines, ratchets, batteries, etc. We analyze how these devices can outperform classical analogues, identifying which aspects of quantum theory power the outperformance. This question and these tasks contrast with the questions and tasks of many non-quantum-thermodynamicists who use statistical mechanics. They often calculate response functions and (e.g., ground-state) properties of Hamiltonians.

These goals of characterizing what nonclassicality is and what it can achieve in thermodynamic contexts resemble upshots of quantum computing and cryptography. As a 21st-century quantum information scientist, I understand what makes quantum theory quantum partially by understanding which problems quantum computers can solve efficiently and classical computers can’t. Similarly, I understand what makes quantum theory quantum partially by understanding how much more work you can extract from a singlet \frac{1}{ \sqrt{2} } ( | 0 1 \rangle - |1 0 \rangle ) (a maximally entangled state of two qubits) than from a product state in which the reduced states have the same forms as in the singlet, \frac{1}{2} ( | 0 \rangle \langle 0 | + | 1 \rangle \langle 1 | ).

As quantum thermodynamics shares its operational approach with quantum information theory, quantum thermodynamicists use mathematical tools developed in quantum information theory. An example consists of generalized entropies. Entropies quantify the optimal efficiency with which we can perform information-processing and thermodynamic tasks, such as data compression and work extraction.

Most statistical-mechanics researchers use just the Shannon and von Neumann entropies, H_{\rm Sh} and H_{\rm vN}, and perhaps the occasional relative entropy. These entropies quantify optimal efficiencies in large-system limits, e.g., as the number of messages compressed approaches infinity and in the thermodynamic limit.

Other entropic quantities have been defined and explored over the past two decades, in quantum and classical information theory. These entropies quantify the optimal efficiencies with which tasks can be performed (i) if the number of systems processed or the number of trials is arbitrary, (ii) if the systems processed share correlations, (iii) in the presence of “quantum side information” (if the system being used as a resource is entangled with another system, to which an agent has access), or (iv) if you can tolerate some probability \varepsilon that you fail to accomplish your task. Instead of limiting ourselves to H_{\rm Sh} and H_{\rm vN}, we use also “\varepsilon-smoothed entropies,” Rényi divergences, hypothesis-testing entropies, conditional entropies, etc.

Another hallmark of quantum thermodynamics is results’ generality and simplicity. Thermodynamics characterizes a system with a few macroscopic observables, such as temperature, volume, and particle number. The simplicity of some quantum thermodynamics served a chemist collaborator and me, as explained in the introduction of https://arxiv.org/abs/1811.06551.

Yoram’s question reminded me of one reason why, as an undergrad, I adored studying physics in a liberal-arts college. I ate dinner and took walks with students majoring in economics, German studies, and Middle Eastern languages. They described their challenges, which I analyzed with the physics mindset that I was acquiring. We then compared our approaches. Encountering other disciplines’ perspectives helped me recognize what tools I was developing as a budding physicist. How can we know our corner of the world without stepping outside it and viewing it as part of a landscape?

Plane

1The title epitomizes clarity and simplicity. And I have trouble resisting anything advertised as “the information-theoretic approach to such-and-such.”

The importance of being open

Barcelona refused to stay indoors this May.

Merchandise spilled outside shops onto the streets, restaurateurs parked diners under trees, and ice-cream cones begged to be eaten on park benches. People thronged the streets, markets filled public squares, and the scents of flowers wafted from vendors’ stalls. I couldn’t blame the city. Its sunshine could have drawn Merlin out of his crystal cave. Insofar as a city lives, Barcelona epitomized a quotation by thermodynamicist Ilya Prigogine: “The main character of any living system is openness.”

Prigogine (1917–2003), who won the Nobel Prize for chemistry, had brought me to Barcelona. I was honored to receive, at the Joint European Thermodynamics Conference (JETC) there, the Ilya Prigogine Prize for a thermodynamics PhD thesis. The JETC convenes and awards the prize biennially; the last conference had taken place in Budapest. Barcelona suited the legacy of a thermodynamicist who illuminated open systems.

IMG_0324

The conference center. Not bad, eh?

Ilya Prigogine began his life in Russia, grew up partially in Germany, settled in Brussels, and worked at American universities. His nobelprize.org biography reveals a mind open to many influences and disciplines: Before entering university, his “interest was more focused on history and archaeology, not to mention music, especially piano.” Yet Prigogine pursued chemistry. 

He helped extend thermodynamics outside equilibrium. Thermodynamics is the study of energy, order, and time’s arrow in terms of large-scale properties, such as temperature, pressure, and volume. Many physicists think that thermodynamics describes only equilibrium. Equilibrium is a state of matter in which (1) large-scale properties remain mostly constant and (2) stuff (matter, energy, electric charge, etc.) doesn’t flow in any particular direction much. Apple pies reach equilibrium upon cooling on a countertop. When I’ve described my research as involving nonequilibrium thermodynamics, some colleagues have asked whether I’ve used an oxymoron. But “nonequilibrium thermodynamics” appears in Prigogine’s Nobel Lecture. 

Prigogine photo

Ilya Prigogine

Another Nobel laureate, Lars Onsager, helped extend thermodynamics a little outside equilibrium. He imagined poking a system gently, as by putting a pie on a lukewarm stovetop or a magnet in a weak magnetic field. (Experts: Onsager studied the linear-response regime.) You can read about his work in my blog post “Long live Yale’s cemetery.” Systems poked slightly out of equilibrium tend to return to equilibrium: Equilibrium is stable. Systems flung far from equilibrium, as Prigogine showed, can behave differently. 

A system can stay far from equilibrium by interacting with other systems. Imagine placing an apple pie atop a blistering stove. Heat will flow from the stove through the pie into the air. The pie will stay out of equilibrium due to interactions with what we call a “hot reservoir” (the stove) and a “cold reservoir” (the air). Systems (like pies) that interact with other systems (like stoves and air), we call “open.”

You and I are open: We inhale air, ingest food and drink, expel waste, and radiate heat. Matter and energy flow through us; we remain far from equilibrium. A bumper sticker in my high-school chemistry classroom encapsulated our status: “Old chemists don’t die. They come to equilibrium.” We remain far from equilibrium—alive—because our environment provides food and absorbs heat. If I’m an apple pie, the yogurt that I ate at breakfast serves as my stovetop, and the living room in which I breakfasted serves as the air above the stove. We live because of our interactions with our environments, because we’re open. Hence Prigogine’s claim, “The main character of any living system is openness.”

Apple pie

The author

JETC 2019 fostered openness. The conference sessions spanned length scales and mass scales, from quantum thermodynamics to biophysics to gravitation. One could arrive as an expert in cell membranes and learn about astrophysics.

I remain grateful for the prize-selection committee’s openness. The topics of earlier winning theses include desalination, colloidal suspensions, and falling liquid films. If you tipped those topics into a tube, swirled them around, and capped the tube with a kaleidoscope glass, you might glimpse my thesis’s topic, quantum steampunk. Also, of the nine foregoing Prigogine Prize winners, only one had earned his PhD in the US. I’m grateful for the JETC’s consideration of something completely different.

When Prigogine said, “openness,” he referred to exchanges of energy and mass. Humans can exhibit openness also to ideas. The JETC honored Prigogine’s legacy in more ways than one. Here’s hoping I live up to their example.

IMG_0349

Outside La Sagrada Familia

Quantum information in quantum cognition

Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care about progress. Whether quantum physics could influence cognition much.

Quantum physics influences cognition insofar as (i) quantum physics prevents atoms from imploding and (ii) implosion inhabits atoms from contributing to cognition. But most physicists believe that useful entanglement can’t survive in brains. Entanglement consists of correlations shareable by quantum systems and stronger than any achievable by classical systems. Useful entanglement dies quickly in hot, wet, random environments. 

Brains form such environments. Imagine injecting entangled molecules A and B into someone’s brain. Water, ions, and other particles would bombard the molecules. The higher the temperature, the heavier the bombardment. The bombardiers would entangle with the molecules via electric and magnetic fields. Each molecule can share only so much entanglement. The more A entangled with the environment, the less A could remain entangled with B. A would come to share a tiny amount of entanglement with each of many particles. Such tiny amounts couldn’t accomplish much. So quantum physics seems unlikely to affect cognition significantly.

Lances

Do not touch.

Yet my PhD advisor, John Preskill, encouraged me to consider whether the possibility interested me.

Try some completely different research, he said. Take a risk. If it doesn’t pan out, fine. People don’t expect much of grad students, anyway. Have you seen Matthew Fisher’s paper about quantum cognition? 

Matthew Fisher is a theoretical physicist at the University of California, Santa Barbara. He has plaudits out the wazoo, many for his work on superconductors. A few years ago, Matthew developed an interest in biochemistry. He knew that most physicists doubt whether quantum physics could affect cognition much. But suppose that it could, he thought. How could it? Matthew reverse-engineered a mechanism, in a paper published by Annals of Physics in 2015.

A PhD student shouldn’t touch such research with a ten-foot radio antenna, says conventional wisdom. But I trust John Preskill in a way in which I trust no one else on Earth.

I’ll look at the paper, I said.

Risk

Matthew proposed that quantum physics could influence cognition as follows. Experimentalists have performed quantum computation using one hot, wet, random system: that of nuclear magnetic resonance (NMR). NMR is the process that underlies magnetic resonance imaging (MRI), a technique used to image people’s brains. A common NMR system consists of high-temperature liquid molecules. The molecules consists of atoms whose nuclei have quantum properties called spin. The nuclear spins encode quantum information (QI).

Nuclear spins, Matthew reasoned, might store QI in our brains. He catalogued the threats that could damage the QI. Hydrogen ions, he concluded, would threaten the QI most. They could entangle with (decohere) the spins via dipole-dipole interactions.

How can a spin avoid the threats? First, by having a quantum number s = 1/2. Such a quantum number zeroes out the nuclei’s electric quadrupole moments. Electric-quadrupole interactions can’t decohere such spins. Which biologically prevalent atoms have s = 1/2 nuclear spins? Phosphorus and hydrogen. Hydrogen suffers from other vulnerabilities, so phosphorus nuclear spins store QI in Matthew’s story. The spins serve as qubits, or quantum bits.

How can a phosphorus spin avoid entangling with other spins via magnetic dipole-dipole interactions? Such interactions depend on the spins’ orientations relative to their positions. Suppose that the phosphorus occupies a small molecule that tumbles in biofluids. The nucleus’s position changes randomly. The interaction can average out over tumbles.

The molecule contains atoms other than phosphorus. Those atoms have nuclei whose spins can interact with the phosphorus spins, unless every threatening spin has a quantum number s = 0. Which biologically prevalent atoms have s = 0 nuclear spins? Oxygen and calcium. The phosphorus should therefore occupy a molecule with oxygen and calcium.

Matthew designed this molecule to block decoherence. Then, he found the molecule in the scientific literature. The structure, {\rm Ca}_9 ({\rm PO}_4)_6, is called a Posner cluster or a Posner molecule. I’ll call it a Posner, for short. Posners appear to exist in simulated biofluids, fluids created to mimic the fluids in us. Posners are believed to exist in us and might participate in bone formation. According to Matthew’s estimates, Posners might protect phosphorus nuclear spins for up to 1-10 days.

Posner 2

Posner molecule (image courtesy of Swift et al.)

How can Posners influence cognition? Matthew proposed the following story.

Adenosine triphosphate (ATP) is a molecule that fuels biochemical reactions. “Triphosphate” means “containing three phosphate ions.” Phosphate ({\rm PO}_4^{3-}) consists of one phosphorus atom and three oxygen atoms. Two of an ATP molecule’s phosphates can break off while remaining joined to each other.

The phosphate pair can drift until encountering an enzyme called pyrophosphatase. The enzyme can break the pair into independent phosphates. Matthew, with Leo Radzihovsky, conjectured that, as the pair breaks, the phosphorus nuclear spins are projected onto a singlet. This state, represented by \frac{1}{ \sqrt{2} } ( | \uparrow \downarrow \rangle - | \downarrow \uparrow \rangle ), is maximally entangled. 

Imagine many entangled phosphates in a biofluid. Six phosphates can join nine calcium ions to form a Posner molecule. The Posner can share up to six singlets with other Posners. Clouds of entangled Posners can form.

One clump of Posners can enter one neuron while another clump enters another neuron. The protein VGLUT, or BNPI, sits in cell membranes and has the potential to ferry Posners in. The neurons will share entanglement. Imagine two Posners, P and Q, approaching each other in a neuron N. Quantum-chemistry calculations suggest that the Posners can bind together. Suppose that P shares entanglement with a Posner P’ in a neuron N’, while Q shares entanglement with a Posner Q’ in N’. The entanglement, with the binding of P to Q, can raise the probability that P’ binds to Q’.

Bound-together Posners will move slowly, having to push much water out of the way. Hydrogen and magnesium ions can latch onto the slow molecules easily. The Posners’ negatively charged phosphates will attract the {\rm H}^+ and {\rm Mg}^{2+} as the phosphates attract the Posner’s {\rm Ca}^{2+}. The hydrogen and magnesium can dislodge the calcium, breaking apart the Posners. Calcium will flood neurons N and N’. Calcium floods a neuron’s axion terminal (the end of the neuron) when an electrical signal reaches the axion. The flood induces the neuron to release neurotransmitters. Neurotransmitters are chemicals that travel to the next neuron, inducing it to fire. So entanglement between phosphorus nuclear spins in Posner molecules might stimulate coordinated neuron firing.

Neurons

Does Matthew’s story play out in the body? We can’t know till running experiments and analyzing the results. Experiments have begun: Last year, the Heising-Simons Foundation granted Matthew and collaborators $1.2 million to test the proposal.

Suppose that Matthew conjectures correctly, John challenged me, or correctly enough. Posner molecules store QI. Quantum systems can process information in ways in which classical systems, like laptops, can’t. How adroitly can Posners process QI?

I threw away my iron-tipped medieval lance in year five of my PhD. I left Caltech for a five-month fellowship, bent on returning with a paper with which to answer John. I did, and Annals of Physics published the paper this month.

Digest image

I had the fortune to interest Elizabeth Crosson in the project. Elizabeth, now an assistant professor at the University of New Mexico, was working as a postdoc in John’s group. Both of us are theorists who specialize in QI theory. But our backgrounds, skills, and specialties differ. We complemented each other while sharing a doggedness that kept us emailing, GChatting, and Google-hangout-ing at all hours.

Elizabeth and I translated Matthew’s biochemistry into the mathematical language of QI theory. We dissected Matthew’s narrative into a sequence of biochemical steps. We ascertained how each step would transform the QI encoded in the phosphorus nuclei. Each transformation, we represented with a piece of math and with a circuit-diagram element. (Circuit-diagram elements are pictures strung together to form circuits that run algorithms.) The set of transformations, we called Posner operations.

Imagine that you can perform Posner operations, by preparing molecules, trying to bind them together, etc. What QI-processing tasks can you perform? Elizabeth and I found applications to quantum communication, quantum error detection, and quantum computation. Our results rest on the assumption—possibly inaccurate—that Matthew conjectures correctly. Furthermore, we characterized what Posners could achieve if controlled. Randomness, rather than control, would direct Posners in biofluids. But what can happen in principle offers a starting point.

First, QI can be teleported from one Posner to another, while suffering noise.1 This noisy teleportation doubles as superdense coding: A trit is a random variable that assumes one of three possible values. A bit is a random variable that assumes one of two possible values. You can teleport a trit from one Posner to another effectively, while transmitting a bit directly, with help from entanglement. 

Teleport

Second, Matthew argued that Posners’ structures protect QI. Scientists have developed quantum error-correcting and -detecting codes to protect QI. Can Posners implement such codes, in our model? Yes: Elizabeth and I (with help from erstwhile Caltech postdoc Fernando Pastawski) developed a quantum error-detection code accessible to Posners. One Posner encodes a logical qutrit, the quantum version of a trit. The code detects any error that slams any of the Posner’s six qubits.

Third, how complicated an entangled state can Posner operations prepare? A powerful one, we found: Suppose that you can measure this state locally, such that earlier measurements’ outcomes affect which measurements you perform later. You can perform any quantum computation. That is, Posner operations can prepare a state that fuels universal measurement-based quantum computation.

Finally, Elizabeth and I quantified effects of entanglement on the rate at which Posners bind together. Imagine preparing two Posners, P and P’, that share entanglement only with other particles. If the Posners approach each other with the right orientation, they have a 33.6% chance of binding, in our model. Now, suppose that every qubit in P is maximally entangled with a qubit in P’. The binding probability can rise to 100%.

Circuit

Elizabeth and I recast as a quantum circuit a biochemical process discussed in Matthew Fisher’s 2015 paper.

I feared that other scientists would pooh-pooh our work as crazy. To my surprise, enthusiasm flooded in. Colleagues cheered the risk on a challenge in an emerging field that perks up our ears. Besides, Elizabeth’s and my work is far from crazy. We don’t assert that quantum physics affects cognition. We imagine that Matthew conjectures correctly, acknowledging that he might not, and explore his proposal’s implications. Being neither biochemists nor experimentalists, we restrict our claims to QI theory.

Maybe Posners can’t protect coherence for long enough. Would inaccuracy of Matthew’s beach our whale of research? No. Posners prompted us to propose ideas and questions within QI theory. For instance, our quantum circuits illustrate interactions (unitary gates, to experts) interspersed with measurements implemented by the binding of Posners. The circuits partially motivated a subfield that emerged last summer and is picking up speed: Consider interspersing random unitary gates with measurements. The unitaries tend to entangle qubits, whereas the measurements disentangle. Which influence wins? Does the system undergo a phase transition from “mostly entangled” to “mostly unentangled” at some measurement frequency? Researchers from Santa Barbara to Colorado; MIT; Oxford; Lancaster, UK; Berkeley; Stanford; and Princeton have taken up the challenge.  

A physics PhD student, conventional wisdom says, shouldn’t touch quantum cognition with a Swiss guard’s halberd. I’m glad I reached out: I learned much, contributed to science, and had an adventure. Besides, if anyone disapproves of daring, I can blame John Preskill.

Lance

Annals of Physics published “Quantum information in the Posner model of quantum cognition” here. You can find the arXiv version here and can watch a talk about our paper here. 

1Experts: The noise arises because, if two Posners bind, they effectively undergo a measurement. This measurement transforms a subspace of the two-Posner Hilbert space as a coarse-grained Bell measurement. A Bell measurement yields one of four possible outcomes, or two bits. Discarding one of the bits amounts to coarse-graining the outcome. Quantum teleportation involves a Bell measurement. Coarse-graining the measurement introduces noise into the teleportation.

Quantum Information Meets Quantum Matter: Now Published!

Two things you should know about me are: (1) I have unbounded admiration for scientists who can actually finish writing a book, and (2) I’m a firm believer that exciting progress can be ignited when two fields fuse together. So I’m doubly thrilled that Quantum Information Meets Quantum Matter, by IQIM physicist Xie Chen and her colleagues Bei Zeng, Duan-Lu Zhou, and Xiao-Gang Wen, has now been published by Springer.

The authors kindly invited me to write a foreword for the book, which I was happy to contribute. That foreword is reproduced here, with the permission of the publisher.

Foreword

In 1989 I attended a workshop at the University of Minnesota. The organizers had hoped the workshop would spawn new ideas about the origin of high-temperature superconductivity, which had recently been discovered. But I was especially impressed by a talk about the fractional quantum Hall effect by a young physicist named Xiao-Gang Wen.

From Wen I heard for the first time about a concept called topological order. He explained that for some quantum phases of two-dimensional matter the ground state becomes degenerate when the system resides on a surface of nontrivial topology such as a torus, and that the degree of degeneracy provides a useful signature for distinguishing different phases. I was fascinated.

Up until then, studies of phases of matter and the transitions between them usually built on principles annunciated decades earlier by Lev Landau. Landau had emphasized the crucial role of symmetry, and of local order parameters that distinguish different symmetry realizations. Though much of what Wen said went over my head, I did manage to glean that he was proposing a way to distinguish quantum phases founded on much different principles that Landau’s. As a particle physicist I deeply appreciated the power of Landau theory, but I was also keenly aware that the interface of topology and physics had already yielded many novel and fruitful insights.

Mulling over these ideas on the plane ride home, I scribbled a few lines of verse:

Now we are allowed
To disavow Landau.
Wow …

Without knowing where it might lead, one could sense the opening of a new chapter.

At around that same time, another new research direction was beginning to gather steam, the study of quantum information. Richard Feynman and Yuri Manin had suggested that a computer processing quantum information might perform tasks beyond the reach of ordinary digital computers. David Deutsch formalized the idea, which attracted the attention of computer scientists, and eventually led to Peter Shor’s discovery that a quantum computer can factor large numbers in polynomial time. Meanwhile, Alexander Holevo, Charles Bennett and others seized the opportunity to unify Claude Shannon’s information theory with quantum physics, erecting new schemes for quantifying quantum entanglement and characterizing processes in which quantum information is acquired, transmitted, and processed.

The discovery of Shor’s algorithm caused a burst of excitement and activity, but quantum information science remained outside the mainstream of physics, and few scientists at that time glimpsed the rich connections between quantum information and the study of quantum matter. One notable exception was Alexei Kitaev, who had two remarkable insights in the 1990s. He pointed out that finding the ground state energy of a quantum system defined by a “local” Hamiltonian, when suitably formalized, is as hard as any problem whose solution can be verified with a quantum computer. This idea launched the study of Hamiltonian complexity. Kitaev also discerned the relationship between Wen’s concept of topological order and the quantum error-correcting codes that can protect delicate quantum superpositions from the ravages of environmental decoherence. Kitaev’s notion of a topological quantum computer, a mere theorist’s fantasy when proposed in 1997, is by now pursued in experimental laboratories around the world (though the technology still has far to go before truly scalable quantum computers will be capable of addressing hard problems).

Thereafter progress accelerated, led by a burgeoning community of scientists working at the interface of quantum information and quantum matter. Guifre Vidal realized that many-particle quantum systems that are only slightly entangled can be succinctly described using tensor networks. This new method extended the reach of mean-field theory and provided an illuminating new perspective on the successes of the Density Matrix Renormalization Group (DMRG). By proving that the ground state of a local Hamiltonian with an energy gap has limited entanglement (the area law), Matthew Hastings showed that tensor network tools are widely applicable. These tools eventually led to a complete understanding of gapped quantum phases in one spatial dimension.

The experimental discovery of topological insulators focused attention on the interplay of symmetry and topology. The more general notion of a symmetry-protected topological (SPT) phase arose, in which a quantum system has an energy gap in the bulk but supports gapless excitations confined to its boundary which are protected by specified symmetries. (For topological insulators the symmetries are particle-number conservation and time-reversal invariance.) Again, tensor network methods proved to be well suited for establishing a complete classification of one-dimensional SPT phases, and guided progress toward understanding higher dimensions, though many open questions remain.

We now have a much deeper understanding of topological order than when I first heard about it from Wen nearly 30 years ago. A central new insight is that topologically ordered systems have long-range entanglement, and that the entanglement has universal properties, like topological entanglement entropy, which are insensitive to the microscopic details of the Hamiltonian. Indeed, topological order is an intrinsic property of a quantum state and can be identified without reference to any particular Hamiltonian at all. To understand the meaning of long-range entanglement, imagine a quantum computer which applies a sequence of geometrically local operations to an input quantum state, producing an output product state which is completely disentangled. If the time required to complete this disentangling computation is independent of the size of the system, then we say the input state is short-ranged entangled; otherwise it is long-range entangled. More generally (loosely speaking), two states are in different quantum phases if no constant-time quantum computation can convert one state to the other. This fundamental connection between quantum computation and quantum order has many ramifications which are explored in this book.

When is the right time for a book that summarizes the status of an ongoing research area? It’s a subtle question. The subject should be sufficiently mature that enduring concepts and results can be identified and clearly explained. If the pace of progress is sufficiently rapid, and the topics emphasized are not well chosen, then an ill-timed book might become obsolete quickly. On the other hand, the subject ought not to be too mature; only if there are many exciting open questions to attack will the book be likely to attract a sizable audience eager to master the material.

I feel confident that Quantum Information Meets Quantum Matter is appearing at an opportune time, and that the authors have made wise choices about what to include. They are world-class experts, and are themselves responsible for many of the scientific advances explained here. The student or senior scientist who studies this book closely will be well grounded in the tools and ideas at the forefront of current research at the confluence of quantum information science and quantum condensed matter physics.

Indeed, I expect that in the years ahead a steadily expanding community of scientists, including computer scientists, chemists, and high-energy physicists, will want to be well acquainted with the ideas at the heart of Quantum Information Meets Quantum Matter. In particular, growing evidence suggests that the quantum physics of spacetime itself is an emergent manifestation of long-range quantum entanglement in an underlying more fundamental quantum theory. More broadly, as quantum technology grows ever more sophisticated, I believe that the theoretical and experimental study of highly complex many-particle systems will be an increasingly central theme of 21st century physical science. It that’s true, Quantum Information Meets Quantum Matter is bound to hold an honored place on the bookshelves of many scientists for years to come.

John Preskill
Pasadena, California
September 2018

 

 

Long live Yale’s cemetery

Call me morbid, but, the moment I arrived at Yale, I couldn’t wait to visit the graveyard.

I visited campus last February, to present the Yale Quantum Institute (YQI) Colloquium. The YQI occupies a building whose stone exterior honors Yale’s Gothic architecture and whose sleekness defies it. The YQI has theory and experiments, seminars and colloquia, error-correcting codes and small-scale quantum computers, mugs and laptop bumper stickers. Those assets would have drawn me like honey. But my host, Steve Girvin, piled molasses, fudge, and cookie dough on top: “you should definitely reserve some time to go visit Josiah Willard Gibbs, Jr., Lars Onsager, and John Kirkwood in the Grove Street Cemetery.”

Laptop

Gibbs, Onsager, and Kirkwood pioneered statistical mechanics. Statistical mechanics is the physics of many-particle systems, energy, efficiency, and entropy, a measure of order. Statistical mechanics helps us understand why time flows in only one direction. As a colleague reminded me at a conference about entropy, “You are young. But you will grow old and die.” That conference featured a field trip to a cemetery at the University of Cambridge. My next entropy-centric conference took place next to a cemetery in Banff, Canada. A quantum-thermodynamics conference included a tour of an Oxford graveyard.1 (That conference reincarnated in Santa Barbara last June, but I found no cemeteries nearby. No wonder I haven’t blogged about it.) Why shouldn’t a quantum-thermodynamics colloquium lead to the Grove Street Cemetery?

Building

Home of the Yale Quantum Institute

The Grove Street Cemetery lies a few blocks from the YQI. I walked from the latter to the former on a morning whose sunshine spoke more of springtime than of February. At one entrance stood a gatehouse that looked older than many of the cemetery’s residents.

“Can you tell me where to find Josiah Willard Gibbs?” I asked the gatekeepers. They handed me a map, traced routes on it, and dispatched me from their lodge. Snow had fallen the previous evening but was losing its battle against the sunshine. I sloshed to a pathway labeled “Locust,” waded along Locust until passing Myrtle, and splashed back and forth until a name caught my eye: “Gibbs.” 

Entrance

One entrance of the Grove Street Cemetery

Josiah Willard Gibbs stamped his name across statistical mechanics during the 1800s. Imagine a gas in a box, a system that illustrates much of statistical mechanics. Suppose that the gas exchanges heat with a temperature-T bath through the box’s walls. After exchanging heat for a long time, the gas reaches thermal equilibrium: Large-scale properties, such as the gas’s energy, quit changing much. Imagine measuring the gas’s energy. What probability does the measurement have of outputting E? The Gibbs distribution provides the answer, e^{ - E / (k_{\rm B} T) } / Z. The k_{\rm B} denotes Boltzmann’s constant, a fundamental constant of nature. The Z denotes a partition function, which ensures that the probabilities sum to one.

Gibbs lent his name to more than probabilities. A function of probabilities, the Gibbs entropy, prefigured information theory. Entropy features in the Gibbs free energy, which dictates how much work certain thermodynamic systems can perform. A thermodynamic system has many properties, such as temperature and pressure. How many can you control? The answer follows from the Gibbs-Duheim relation. You’ll be able to follow the Gibbs walk, a Yale alumnus tells me, once construction on Yale’s physical-sciences complex ends.

Gibbs 1

Back I sloshed along Locust Lane. Turning left onto Myrtle, then right onto Cedar, led to a tree that sheltered two tombstones. They looked like buddies about to throw their arms around each other and smile for a photo. The lefthand tombstone reported four degrees, eight service positions, and three scientific honors of John Gamble Kirkwood. The righthand tombstone belonged to Lars Onsager:

NOBEL LAUREATE*

[ . . . ]

*ETC.

Onsager extended thermodynamics beyond equilibrium. Imagine gently poking one property of a thermodynamic system. For example, recall the gas in a box. Imagine connecting one end of the box to a temperature-T bath and the other end to a bath at a slightly higher temperature, T' \gtrsim T. You’ll have poked the system’s temperature out of equilibrium. Heat will flow from the hotter bath to the colder bath. Particles carry the heat, energy of motion. Suppose that the particles have electric charges. An electric current will flow because of the temperature difference. Similarly, heat can flow because of an electric potential difference, or a pressure difference, and so on. You can cause a thermodynamic system’s elbow to itch, Onsager showed, by tickling the system’s ankle.

To Onsager’s left lay John Kirkwood. Kirkwood had defined a quasiprobability distribution in 1933. Quasiprobabilities resemble probabilities but can assume negative and nonreal values. These behaviors can signal nonclassical physics, such as the ability to outperform classical computers. I generalized Kirkwood’s quasiprobability with collaborators. Our generalized quasiprobability describes quantum chaos, thermalization, and the spread of information through entanglement. Applying the quasiprobability across theory and experiments has occupied me for two-and-a-half years. Rarely has a tombstone pleased anyone as much as Kirkwood’s tickled me.

Kirkwood and Onsager

The Grove Street Cemetery opened my morning with a whiff of rosemary. The evening closed with a shot of adrenaline. I met with four undergrad women who were taking Steve Girvin’s course, an advanced introduction to physics. I should have left the conversation bled of energy: Since visiting the cemetery, I’d held six discussions with nine people. But energy can flow backward. The students asked how I’d come to postdoc at Harvard; I asked what they might major in. They described the research they hoped to explore; I explained how I’d constructed my research program. They asked if I’d had to work as hard as they to understand physics; I confessed that I might have had to work harder.

I left the YQI content, that night. Such a future deserves its past; and such a past, its future.

WIP

With thanks to Steve Girvin, Florian Carle, and the Yale Quantum Institute for their hospitality.

1Thermodynamics is a physical theory that emerges from statistical mechanics.

Science Communication Camp: a unique experience

Take a group of curious, open-minded people, place them in an idyllic setting and let them brainstorm on various facets of science communication for a weekend. If you also supplement this with impeccable organization and lively, cool and interesting hosts, you have the recipe for ultimate success!

The 4th annual Science Communication Camp took place at the Brandeis-Bardin campus of the American Jewish University on November 2nd-4th. The warm welcome by the organizers at the registration desk, the settling in at the on-campus, cozy rooms and the campus tour set the tone for the weekend. The guests? Research scientists, scientists that do outreach via academia, freelance science writers, policy makers on health and other scientific issues, science museum personnel, people doing research for magazines like National Geographic, YouTubers, educators, you name it!

I was excited to attend because although I am a biologist working in a lab, right now, one of my goals is to get more women interested in science and show non-science people how exciting our work can be. What a diverse and interesting group of people with whom to exchange views!

The weekend included a series of workshops, along with outdoor activities and group sessions – all capped off by a campfire on the final night. During the very lively and witty workshop on science script-writing, Teagan Wall let us in on her world of TV script-writing and meticulously showed us how to break down a scenario. Collectively, we came up with an inspiring episode of Bill Nye Saves the World (Teagan has written for that show). We included a humorous discussion about conventional and unconventional batteries and also raised awareness about how many smartphone batteries are thrown away.

Rachel Ignotofsky, author and illustrator of the magnificent bestseller book Women in Science, 50 Fearless Pioneers Who Changed the World gave a passionate, vivid and fun introduction into the world of science illustration. As a biologist, I really liked Rachel’s illustrations of lab equipment.

In her keynote speech, Maryn McKennna, author of widely read books such as Superbug and Big Chicken, walked us through her fascinating career that got her from pure news journalism to science journalism, doing research all around the globe.

Entertainment wasn’t missing from the mix. UCLA earth scientists, wildlife preservation experts, and other scientists, invited us to delve into their world. The highlight for me was the unique opportunity to touch a fragment of an asteroid that was magnetic! The night magic continued while Magician Siegfried Tiebe presented amazing tricks with humor and lightness, like a pleasant breeze.

The campfire, s’mores and singing in a small group, accompanied by the melodies of a lovely guitar and the stargazing (for the few night owls), concluded the final night in an ideal way.

Saying goodbye had a bittersweet feeling, but I was filled with new ideas, gifted with a broader outlook and also had my suitcase filled with three new books that were kindly provided to us.

Congratulations to IQIM for sponsoring such a great event that allows people from the Caltech community to broaden their horizons and launch, or better define, their path in the science communication realm.