Neumann’s early papers on the subject, and take in the substantial body of literature associated with quantum logic. Unfortunately, in spite of considerable mathematical ingenuity, these efforts never quite succeeded, and the search for a logical, operational or probabilistic foundation for QM had lost most of its momentum by the early 1980s.

The situation changed, dramatically, around the turn of the present century, owing to the development of quantum information theory (QIT). This provided just enough of a shift of viewpoint to enable considerable progress. First, QIT considers finite-dimensional systems, making these a respectable target. Secondly, QIT makes essential use of properties of composite systems and entangled states, making it seem reasonable to treat certain properties of such states as postulates. The power of such an approach was first demonstrated by Lucien Hardy in a pioneering paper entitled “quantum theory from five simple axioms”. This was followed by a spate of papers by various authors, including those of the present book, in which finite-dimensional quantum mechanics is deduced from various (but similar) packages of more or less operational assumptions.

One key idea exploited by all of these papers is that systems having a the same “information content” should be physically equivalent. Here information content refers to the maximum number of states that can be sharply distinguished by a single trial of a single measurement. Another is “locality” (or tomographic locality), which is the doctrine that the state of a composite system should depend only on the joint probabilities it assigns to the results of measurements on the two subsystems. Most of the cited papers also rely on a symmetry assumption, requiring that any two pure states should be related by a reversible physical transformation. The authors of this book replace this with a stronger purification principle, requiring that any state of any system A should be representable as the marginal, or reduced, state of a pure bipartite state on a compound system AB consisting of the given system together with an ancilla, B, and that this should be unique up to a reversible transformation on B. A rather amazing amount of structure flows from this one assumption.

This is first book-length treatment of these ideas. In that sense, it is a research monograph. However, very agreeably, it is presented as a textbook: explanations and examples are developed in detail, and in an attractive and easy-going style, and there are even exercises! This is a very good thing, and should be more widely imitated. In particular, this manner of presentation makes the book accessible to graduate students, or even well-prepared undergraduates, while also making it comparatively easy reading for the physicist of mathematician interested in an introduction to this area, and even for the expert who wants to understand the details of the authors’ particular approach.

The book is divided in to four parts. Part I deals with finite-dimensional quantum mechanics, or perhaps better to say, quantum information theory, presented in a style that emphasizes the convex geometry of the state space (that is, the space of density operators) and properties of completely positive maps. Along the way, the authors identify several features of this theory that, expressible in purely operational/probabilistic language, can serve as postulates for a more abstract, Hilbert-space independent, information theory. In Parts II and III, the authors give a general account of probabilistic theories satisfying their assumptions, showing convincingly that many well-known quantum information-theoretic phenomena follow naturally (and, in their formulation, elegantly) from these: Teleportation protocols, ensemble steering and much more, receive treatment here. The heart of the book is Chapter 7, in which the authors present the most immediate consequences of the purification postulate. In a deft, almost effortless way, they show, for instance, that the purifying states must have a steering property, that measurement inevitably corresponds to state-disturbance, and that unknown states can be “teleported” through entangled states. Later chapters build on this to recover, not only further standard results from quantum information theory, but also a substantial slice of the spectral theorem, without ever mentioning Hilbert space.

Using this machinery, the authors undertake in Part IV to reconstruct the finite-dimensional version of the standard quantum-mechanical formalism. That is, they show that any theory satisfying the postulates of Section II can be represented in such a way that states are density operators on some finite-dimensional complex Hilbert space, and

all density operators correspond to states; that measurement-outcomes are positive self-adjoint operators bounded by the identity operator (and conversely); and that processes are represented by completely positive mappings (and conversely). Although it requires some work, the proof of this result is elementary, in the sense that it does not lean on any mathematical results not already developed. This is in contrast to other reconstruction theorems. For instance, the quantum-logic approach requires the fundamental theorem of projective geometry, while most of the other post-Hardian reconstructions lean on the classification of compact group actions on spheres.

A striking feature of the book, apparent on nearly every page, is the use of a notation that replaces equations involving tensor products with diagrams. These take up space, and may be a bit off-putting at first for those not familiar with them, but it well repays the small effort needed to master this formalism: once one has learned to trust it (say, by translating a few examples back into equational language), many proofs become so natural as to be almost automatic. The book is well-produced, with an attractive layout and, in view of the complexity of the diagrammatic typesetting remarkably few typos. All in all, the authors are to be congratulated on producing a delightful, inspiring, and persuasive introduction to their way of looking at finite-dimensional quantum theory.

UPDATE: In the first version of this article, the authors were listed in the wrong order. This has been changed to the order they are listed on the book cover.

]]>Review of Hans Christian von Baeyer’s *QBism: The Future of Quantum Physics*

**Kelvin J. McQueen**

Department of Philosophy, Chapman University, Orange, CA, US.

**Contents**

1 Overview

2 Can QBism resolve quantum paradoxes?

3 What does QBism tell us about reality?

4 Does QBism explain why the sun shines?

5 Final thoughts

**1. Overview**

The purpose of this book is to explain Quantum Bayesianism (“QBism”) to ”people without easy access to mathematical formulas and equations” (4-5). Qbism is an interpretation of quantum mechanics that ”doesn’t meddle with the technical aspects of the theory [but instead] reinterprets the fundamental terms of the theory and gives them new meaning” (3). The most important motivation for QBism, enthusiastically stated on the book’s cover, is that QBism provides ”a way past quantum theory’s paradoxes and puzzles” such that much of the weirdness associated with quantum theory ”dissolves under the lens of QBism”.

Could a non-technical book that almost fits in your pocket really succeed in resolving the notorious paradoxes of quantum theory? I believe the answer is: not in this case. There are three primary reasons. Firstly, the argument that QBism solves quantum paradoxes is not convincing. Secondly, it proves difficult to pin down exactly what QBism says. Thirdly, as a scientific theory QBism seems explanatorily inert, which is maybe why the topic of scientific explanation is not broached. Sections 2-4 below discuss each of these problems in turn. However, there is still a wealth of insights that make this book a worthwhile read, and I shall begin with those.

The book is split into four chapters. The first presents eight sections that take the reader on a lively journey through quantum theory. This chapter will prove valuable to a variety of readers. For a general audience, it is one of the best non-technical introductions to quantum physics I have read in some time. For specialists, it illustrates clever methods for explaining quantum theory to beginners.

So much for the `Q’ in QBism. Chapter two presents two sections explaining Bayesian probability theory (the `B’). The first (section 9) sets the stage by challenging common intuitions about the nature of probability e.g. using the paradox of the cube factory. It is then explained how nature can yield surprising demands on correct probability assignments. This is carefully illustrated with Bose-Einstein statistics and the exclusion principle. Finally, the probability theory known as *frequentism* is sharply criticized. Section 10 espouses Bayesian probability theory. Here the central rule for rationally updating one’s probability assignments in light of new evidence – Bayes’ law – is explained and illustrated with care.

My only qualm so far is that the dichotomy between frequentism and Bayesianism is slightly misleading. For much of the book suggests that adopting QBism is a ”decision to switch from the frequentist to the Bayesian interpretation of probability” (132). But there are two forms of Bayesianism – objective and subjective. According to objective Bayesianism, probabilities are real things in nature, while according to subjective Bayesianism, probabilities are the personal degrees of beliefs of agents. Only subjective Bayesianism is consistent with QBism. Moreover, there are other interpretations of probability, such as *the best system’s theory*, which resemble frequentism but are more defensible.

Chapter three is dedicating to explaining QBism and how it resolves the various quantum paradoxes and chapter four specifies various implications of QBism. There is a lot to like about these final two chapters. However, I will focus on the three above mentioned problems: (i) the argument that QBism solves quantum paradoxes is not convincing; (ii) it proves difficult to pin down exactly what QBism says and (iii); as a scientific theory QBism seems explanatorily inert. Let’s take each issue in turn.

**2. Can QBism resolve quantum paradoxes?**

Section 11, ”QBism made explicit”, begins by presenting QBism as a confluence of quantum theory and subjective Bayesianism. QBism is defined by a specific thesis:

”The principal thesis of QBism is simply this: quantum probabilities are numerical measures of personal degrees of belief” (131).

By itself this doesn’t suggest a distinctive interpretation of quantum mechanics. For a number of interpretations may help themselves to this principle (and to Bayesianism more generally). For example, in Bohmian mechanics quantum probabilities only arise due to our ignorance of the initial positions of particles. The probabilities may then be interpreted as the degree to which we believe a particle is in a given location. Moreover, some versions of the many worlds interpretation treat quantum probabilities as numerical measures of personal degrees of belief (where the beliefs concern which branch of the multiverse one is in). So we need to know more in order to individuate QBism as a distinctive interpretation. I will return to this problem in the next section. Let’s first look to the quantum paradoxes.

**The problem of collapse**

The problem of wavefunction collapse is defined as follows: ”there is no mathematical description of how it [collapse] happens in space and time” (132-3). However, in light of the kinds of dynamical collapse theories presented by Pearle, Penrose, Ghirardi, and others, it seems that mathematically describing collapse is not the real problem. The real problem concerns whether collapse *happens*. You might have thought that this problem will eventually get resolved by the ongoing experimental tests for collapse. But QBists have a different kind of solution:

”Qbism solves the problem with ease and elegance. In any experiment the calculated wavefunction furnishes the prior probabilities for empirical observations that may be made later. Once an observation has been made […] new information becomes available to the agent performing the experiment. With this information the agent updates her probability and her wavefunction – instantaneously and without magic. The collapse sheds its mystery. Bayesian updating describes it and finally makes the missing step explicit” (133)

It is unclear how this represents a solution. The assumption seems to be that the concept of collapse arises entirely out of the wavefunction so that just by reinterpreting it we avoid the need for collapse. But the collapse concept arises first and foremost out of our experimental observations. Consider the double-slit experiment with electrons. If one monitors the slits, one eventually sees two bands of hits on the fluorescent screen. If one does not monitor the slits, one instead sees an interference pattern. Why does monitoring the slits make such a striking difference? Does monitoring the slits cause the states of the electrons to collapse from one kind of state into another? If not, what yields the appearance of collapse? Considerations of how the experimenter updates his probability assignments after seeing such results do not seem relevant to the problem.

**The problem of nonlocality**

An example is offered to help the reader understand the QBist account of the apparent collapse of entangled particles:

”Alice, in New York, picks two playing cards, one black and one red, and tucks them into separate unmarked envelopes, which she seals and then shuffles. […] She keeps one in her purse and hands the other one to Bob. Alice then leaves the room and travels to Australia. Before she opens her envelope, her degree of belief that Bob has the red card is 50 percent. But upon arrival, as soon as she looks at her own card she knows what’s in Bob’s envelope twelve thousand miles away, so she updates her degree of belief to either 100 percent or to 0 percent instantaneously. In the meantime Bob’s guess about the color of Alice’s card, whatever it may be, remains unaffected by her actions. There is no miracle.” (133-4)

However, in this classical case we have reason to think that there is a playing card in each envelope at all times during Alice’s flight. This partly explains why Alice is right to update her degree of belief about Bob’s card instantaneously. So there is no problem with this case. But in the quantum case, we have reason to think that Bob’s system did not have any definite value for the measured observable prior to Alice’s measurement. So how can the value of Bob’s system suddenly become predictable for Alice when she learns the value of her system? This stands in need of explanation. Did Alice’s action collapse Bob’s system from a non-definite value to a definite value or not? And if it did not, what explains why it appears that it did? As before, this problem is independent of the wavefunction in that we can define the problem in terms of experimental observations alone. Consequently, a subjective Bayesian interpretation of the wavefunction does not seem to be the right apparatus to solve the problem.

**The problem of Wigner’s friend**

The ”paradox” of Wigner’s friend involves (i) Wigner’s friend measuring the spin of an electron and updating his wavefunction accordingly and (ii) Wigner, who turns his back to the experiment and so describes his friend as being in an entangled superposition. Wigner and his friend therefore have distinct wavefunctions. The paradox is then stated as follows:

”So who’s right? Has the qubit collapsed, or is it still a superposition? As long as the wavefunction is regarded as a real thing or as a description of a real process, the question is no more easily resolved than Bishop Berkeley’s infamous question about the tree in the forest: When a tree falls in the forest and nobody hears it, does it make a sound?” (136)

But this statement seems incorrect. Theories which admit the reality of the wavefunction yield straightforward answers to this question. For example, it is a trivial implication of collapse theories that Wigner is wrong, his friend is right. Still, the QBist ”solution” helps us to further pin down what is distinctive about QBism:

”According to QBism, there is no unique wavefunction. Wavefunctions are not tethered to electrons […] they are assigned by an agent and depend on the total information available to the agent. They are malleable and subjective. In short, wavefunctions and quantum probabilities are Bayesian” (137).

Here we see a statement that makes QBism distinctive: *wavefunctions are neither real nor represent real physical systems*. This is a striking claim that does not follow merely from quantum probabilities being Bayesian. One is left wondering what the motivation for it is. Wavefunctions are our models of particles that are used to predict the behaviour of those particles. If those models do not (even approximately) represent real physical systems then what does?

**The problem of Schrödinger’s cat**

How should we represent reality if not via wavefunctions? This problem for QBism is exacerbated when considering macroscopic superpositions, which is the topic of section 12: ”QBism saves Schrödinger’s cat”. For if Schrödinger’s cat isn’t literally in a superposition of being both alive and dead before the box is opened, as the uncollapsed wavefunction prescribes, then what is its actual state? Despite the claim that ”QBism deals with the story as effortlessly as it disposes of the miracle of wavefunction collapse and the paradox of Wigner’s friend” (141), QBism does not appear to have an answer:

”QBism refuses to describe the cat’s condition before the box is opened and rescues it from being described as hovering in a limbo of living death” (142).

Refusing to describe the cat from being in a given state does not seem to save the cat from being in that state. What is the cat’s condition? Without an answer we have no guarantee that it is not hovering in limbo.

**3. What does QBism tell us about reality?**

Perhaps the demand to know the physical state of Schrödinger’s cat (were we to experimentally realize such a scenario) is asking for too much. Sometimes, when a theoretical problem gets *really* hard, one does not try to solve it, rather, one tries to show that epistemic limitations prevent humans from solving it. We might call this ”dissolving” but not solving the problem. Some have tried to dissolve the notorious mind-body problem, for example. Perhaps QBists are only trying to dissolve the quantum paradoxes?

But we are given no argument for the claim that describing the cat’s condition before the box is opened (for example) is beyond us. Section 12: ”The Roots of QBism” offers quotes from Democritus to Heisenberg, supporting scepticism of ”unvarnished objectivity” (148). But quotes are not arguments. And the major realist interpretations of quantum mechanics, from collapse theories to many worlds theories to hidden variables theories, to retrocausal theories, all evidence our evolving ability to describe cats in any physically possible situation.

Section 14, ”Quantum Weirdness in the Laboratory”, asserts that ”QBism, by foregoing realism of the Einstein, Podolsky, and Rosen kind, provides a simple, convincing way to avoid spooky action at a distance” (169). But as discussed, the fundamental problem is found in the lab, where we observe apparent action at a distance. To solve the problem we need a description of what’s going on that accounts for the appearances without postulating action at a distance. If QBism is to help us with this problem is must start by telling us what exists. Once we know what exists, we can ask whether those things are local.

Section 15, ”All Physics is Local”, is puzzling. It begins well, by describing how general relativity helped remove the action at a distance inherent in Newton’s theory of gravity. It also gives an elegant account of how Feynman diagrams depict the locality of interactions in quantum mechanics. Locality – where interactions only take place at a spacetime point – is a desirable property of physical theories. So we can ask, is QBism a local physical theory? Or to put the question another way:

”Where, according to QBism, are the spots, the loci in Latin, at which interactions take place? The black dots of Feynman diagrams are, after all, not actual points in space-time but mere mathematical devices used for calculating probabilities. In plain words, where, according to QBism, does stuff happen?” (175)

To answer this question von Baeyer first quotes original QBists, Fuchs, Schack, and Mermin:

”QBist quantum mechanics is local because its entire purpose is to enable any single agent to organize her own degrees of belief about the contents of her own personal experience” (175).

To clarify, von Baeyer adds:

”Personal experiences are recorded (located) in the agent’s mind. They follow each other in time but by definition never occur simultaneously in widely separated locations. They are local.” (175-6).

But a natural reading of this statement seems in conflict with neuroscience. The cerebral cortex only becomes animated with consciousness when its nerve cells behave in an orchestrated or integrated manner. A conscious experience is hardly a point-like event. But all this talk of personal experience is beside the point. The question of locality is a question about the world not our conscious minds. Is the world local according to QBism or not? Without a description of reality, it seems we must remain agnostic.

Section 16, ”Belief and Certainty”, attempts to deal with situations in which probability equals unity. The EPR criterion of reality entails that if an electron’s wavefunction is a z-spin eigenstate with eigenvalue +1, then the electron *really is* spin-up about the z axis, whether or not it has been measured yet. But then the wavefunction really does describe the electron, at least in this case. QBists respond by reinterpreting probability 1: ”What does it mean when an agent assigns probability 1 to an event? In the context of Bayesian probability, all it implies is that she is very, very sure that it will occur […] It does not imply anything […] about the actual makeup of the real world” (181). I leave it to the reader to ponder this response.

The final chapter of the book, ”The QBist Worldview”, promises to fill in some details about the QBist ontology. Section 17, ”Physics and Human Experience”, emphasizes how QBism places agents, or users of quantum theory, ”at the center of the action” (194). This is supposed to be in contrast to traditional physics, which ignores agents completely, and instead just describes atoms in the void. But is QBism guilty of the transpose?

Section 18, ”Nature’s Laws”, compares two conceptions of laws of nature. The first states that laws are real things that govern or guide events in the natural world. The second states that natural events are not governed by laws, laws are just our best summaries of regularities and patterns in events. Qbism adopts the latter. But the summarised events refer to conscious experiences.

Section 19, ”The Rock Kicks Back”, gives crucial yet cryptic hints about the intended ontology:

”According to QBism, a measurement does not reveal a preexisting value. Instead, that value is created in the interaction between the quantum system and the agent […] the same kind of fact creation occurs when any two quantum systems happen to come together.” (205-7).

Everyone should agree that new facts are generated by things coming together, at least in this pedestrian sense: if two particles collide, then the sentence ”two particles are rebounding away from each other” may come true.

But I think most would disagree with the first statement and insist that measurements often do reveal preexisting values. For example, if I walk into a room and observe a chair, then the chair was there before I walked in. One wonders whether chairs count as quantum systems in the QBist framework.

QBists appear to want to agree that agents, measuring devices, and measured systems like electrons all exist. We cannot describe the electron, but when an agent interacts with it (via a device), a new fact comes into being, e.g. the fact that the electron is spin-up.

Fact-creation appears to be the QBist’s replacement for collapse. But it looks like this replacement suffers the exact problem that was raised for collapse: ”there is no mathematical description of how it happens in space and time” (132-3). So it becomes difficult to see what advantage QBism has over the orthodox collapse picture espoused by John von Neumann.

**4. Does QBism explain why the sun shines?**

Section 21, ”A Perfect Map?”, asserts that ”Qbism […] implies that science is not about ultimate reality but about what we can reasonably expect” (221), and then argues that this should not be taken as an admission of defeat. Two arguments are offered. Here is one:

”Qbism, by moving physics closer to human thoughts and feelings, may have a better chance than raw materialism to solve the ancient enigma of consciousness, the problem of the relationship between the mind and the brain.” (221).

But a theory which refuses to describe the physical world is hardly going to be able to describe how that physical world generates consciousness. Here is the other:

”QBism doesn’t detract in any way from the immense success of quantum mechanics in helping us understand not only the material world but, through biochemistry and neuroscience, the foundations of the life sciences as well. Knowing what we can reasonably expect and how firmly we should expect it is as close as we can come to understanding and controlling the world.” (221).

This statement addresses the status of scientific explanantion in QBism. But QBism seems explanatorily inert. For scientific explanations typically explain phenomena in terms of underlying mechanisms. Here is a simple example. Why is the Sun able to produce so much energy over such a long period of time? Physicists tend to answer this question with an explanation that goes something like this:

The sun is composed of many little parts, including hydrogen atoms. If hydrogen atoms fuse together they yield helium. The difference in mass between the products and reactants is manifested as the release of large amounts of energy. According to quantum theory, hydrogen atoms are able to get close enough together to fuse *because they undergo quantum tunneling*.

It is not open to the QBist to describe atoms as tunneling, since for QBists tunneling is a psychological phenomenon regarding our degrees of belief. Then what of the explanation? Could the QBist reconstruct the explanation in their own terms? I’m not sure if QBists believe in hydrogen atoms or fusion (as opposed to just the experiences induced by our measurements of them). But assuming they do (the explanations will look worse if they don’t!), the worry is that QBist explanations will inevitably look something like this:

The sun is composed of many little parts, including hydrogen atoms. If hydrogen atoms fuse together they yield helium. The difference in mass between the products and reactants is manifested as the release of large amounts of energy. According to QBism, hydrogen atoms are able to get close enough together to fuse *because we expect them to – indeed we are willing to place bets on it*.

The worry with the latter ”explanation” is that it is tautologous: something should be expected to happen because we should expect it to happen. But what we want to know is *why* we should expect it to happen?

**5. Final thoughts**

I have specified some difficulties with QBism. But to end on a positive note, QBism should be applauded as a breeding ground of ideas for multiple disciplines including physics, philosophy, and mathematics, and von Baeyer’s book offers an account accessible to all.

The final section, section 22 ”The Road Ahead”, rightly notes that ”One of the most important attributes of a new scientific idea is that it should be *heuristic*, leading to further research, inspiring fresh ideas and questions” (225). The further research arising from QBism is the ”program of expressing the quantum rules in terms of probabilities rather than wavefunctions”. Von Baeyer discusses how this program has experienced some success and even shows promise in helping to solve problems in pure mathematics. He even speculates that this program ”may turn out to be the basis of a radically new formulation of quantum mechanics without wavefunctions” (230).

This section was a refreshing one to finish on. It seems that the right way to motivate QBism, is to show that working with it as an assumption can yield unexpected research programs that integrate with other disciplines (e.g. pure mathematics).

In conclusion, due to the three problems mentioned, this book does not provide a convincing case that QBism is ”The Future of Quantum Physics”. But it does provide an outstanding introduction to two of the key components of QBism (quantum theory and subjective Bayesianism), and places the reader into the mind of the QBist in a way that will aid the ongoing debate over its merit. It is a worthwhile read.

]]>You should become part of our team, if one of the following applies to you:

- Either, you are an expert in the theory of quantum information
- Or, you are an expert classical applied network architecture and routing

You should also satisfy both of the following requirements:

- You hold a PhD degree in computer science, electrical engineering, physics or applied mathematics at the time of assuming the position.
- You have an exceptional track record from your previous projects.

The positions are located at QuTech, TU Delft, a world leading institute in quantum technologies. You will join the Quantum Internet Roadmap, working with the theory (software) groups of Stephanie Wehner and David Elkouss. You will also closely collaborate with the experimental (hardware) group of Ronald Hanson.

Deadline: 15 July 2017

Starting date: As soon as possible, negotiable

To apply please use the following form: http://tiny.cc/QuantumInternetPostdoc

]]>Poster abstracts due on May 31, 2017.

More information qec2017.org

]]>Many theoretical challenges need to be solved in order to implement the first quantum networks. In this PhD position, you will have the opportunity to solve some of these practical challenges. You will join the theory group of David Elkouss in QuTech at TU Delft and will work in close collaboration with the experimental groups of Ronald Hanson and Tim Taminiau and with the theory group of Stephanie Wehner.

You have a master’s degree and an exceptional track record in either maths, physics, computer science or electrical engineering. You have demonstrated your abilities in at least one research project. A background in quantum information and/or programming are a plus.

The deadline is May the 1st but applications will be considered until the position is filled.

To apply please email the following documents in pdf format to d(dot)elkousscoronas(at)tudelft(dot)nl:

- CV
- Your complete transcript
- Letter of motivation
- 2 letters of reference from faculty who have supervised you in a project. These should be emailed directly to d(dot)elkousscoronas(at)tudelft(dot)nl and have the subject “Reference for [YourName]”.
- One report from a project that you have done.

Also, while you are sitting through a typical March meeting talk where the speaker tries to give their usual 30min talk in 10min, rushing through a series of incomprehensible slides, or when you have gone back to the hotel early with a Subway sandwich having lost all your friends and colleagues in the morass of physicists, why not distract yourself by giving some quantum games a try? Here are some possibilities:

**Games to be discussed at the March Meeting:**

- Quantum Moves
- qCraft (Minecraft mod)
- MeQanic
- The BIG Bell Test
- Quantum Chess
- Decodoku
- Minecraft PR-Box mod
- Quantum Cats

**Other Quantum Games**

In the rest of this article, I briefly review my top picks for quantum games, bearing in mind that I haven’t played all of them. In particular, since I did not have a 12 year old handy, I have not tried any of the Minecraft mods. Also, Quantum Chess is still in private beta, but you can see an interesting talk on it by its creator Chris Cantwell here, and you can watch Stephen Hawking play Quantum Chess with Paul Rudd (Ant Man) here. Following the style of gaming magazines, I will give each of my picks a seemingly arbitrary score out of 10 for their science, their gameplay, and their sound and graphics.

Quantum games broadly fit into four overlapping categories, and I will review my top pick for each one. The categories are:

**Crowdsourcing Research:** These games aim to use the data generated by humans playing the game to solve research problems in quantum physics. This is the same idea as the well-known FoldIt game, which uses humans to solve protein folding problems.

**Building Intuition:** The idea of these games is to build intuition for how quantum mechanics works by having a game that is built on the rules of an actual quantum mechanical system, without any equations. The aim is not exactly education, but rather to make the abstract features of quantum theory seem more concrete.

**Education:** The aim of these games is to actually teach some quantum mechanics. If a student plays through one of these games, then they ought to be better equipped for their modern physics and quantum mechanics classes. These games might also be used as a supplement in such classes.

**Outreach:** The aim of these games is to get people excited about quantum mechanics by putting some quantum ideas in front of people who might not otherwise see them. If they are educational, then it is only at the popular science level.

**Top Pick for Crowdsourcing Research: Quantum Moves**

Platform: Windows, Linux, Mac, Android, iOS (basically everything)

Project Lead: Jacob Sherson (Aarhus University)

Science: 9

Gameplay: 6

Graphics and sound: 9

The Science:

The aim of Quantum Moves is to help figure out how to move single atoms/ions around in an ion trap using lasers without changing their quantum state. Computer algorithms exist to optimize this, but apparently better results can be obtained by running human-generated solutions through an optimization algorithm.

This game gets top marks for science because it is the only game I am aware of to have resulted in a Nature Publication. The human generated data has been used to build an efficient heuristic optimization algorithm that outperforms other numerical methods. In fact the Science@Home team behind this game have several publications and preprints based on Quantum Moves, they have several other games in development. The most interesting of these Quantum Minds, which is being used by cognitive scientists to study how humans come up with solutions in games like Quantum Moves.

The Game:

The game itself is quite simple. You are presented with a one dimensional curve, which represents the potential of some physical system. Located somewhere along this curve, usually in a potential dip, will be a “liquid” that has funny properties when you move it around. The “liquid” represents the wavefunction of a single atom. You have a cursor, which you can drag around the screen to move another potential dip, which represents the effect of a laser. The aim is to move the “liquid” to a target area while keeping its shape the same as much as possible, i.e. move the atom while keeping the fidelity with (a translated version of) the initial state as high as possible.

The “liquid” has some very counter-intuitive properties that are unlike anything most players will have encountered. Well, it is, after all, a wavefunction and not a liquid, but “liquid” is the terminology used in the game. If you are a quantum physicist, then you will know a few tricks that will help you through the initial levels. For example, by the adiabatic theorem, you know that moving an isolated potential dip with an atom in it very slowly is probably a good idea, and you know that when you want to transfer an atom from one dip to another similarly shaped one then you know that making a symmetric double-well will be good for tunneling. Other than that, the behavior of the “liquid” is, to me at least, extremely unintuitive. It sloshes around unpredictably and it is very difficult to figure out what will work well. A few hints are given on the website, e.g. it turns out that shaking the well from side to side a little as you move it helps to maintain the shape of the wavefunction.

The unintuitive behavior of the “liquid” makes for a steep learning curve, and makes the game not especially fun to play, which is why I have only given it 6 for gameplay. Puzzle games can be placed on a spectrum from concrete to abstract. A concrete puzzle game makes use of things that players already have strong correct intuitions for, and the challenge is just to combine these elements in a clever way. An example of a concrete puzzle game is Lemmings, which uses intuitions like, “if a lemming falls a long way it will splat on the ground and die”. In contrast, an abstract puzzle game makes use of elements and rules that seem completely arbitrary when you first encounter them. You have to learn what the rules even mean and build intuition for them as you go. Quantum Moves, and indeed most quantum puzzlers, are on the extreme abstract end of the spectrum.

An abstract puzzler can be fun to play, but I think that most players would want considerable help in the early levels as an aid to building intuition. It is not too hard to get high scoring solutions on the first couple of levels, but I quickly struggled to get good scores thereafter. My inability to figure out how to improve my scores turned me off the game fairly rapidly. From a science point of view, you obviously want to present the player with hard problems that we do not know how to solve easily, but if you are trying to compete for distracted players with other more fun games then you are quickly going to lose players to other games like Angry Birds. Players who are more persistent or more fond of arbitrary abstract thinking then I am may enjoy this game more than I did.

The graphics and visuals of this game are very good, comparable to professionally produced games that you might play on your smartphone.

**Top Pick for Building Intuition: Decodoku**

Platform: Windows, Mac, Web, Android, iOS

Project Lead: James Wootton (University of Basel)

Science: 9

Gameplay: 8

Graphics and sound: 5

The Science:

There is a large overlap between my game categories, and Decodoku is also a crowdsourcing research game, but its style of gameplay is similar to other building intuition games like MeQanic, and it is more fun than the others I have played, so I decided to put it here. I have not read a technical account of the science behind Decodoku, but from what I can gather it is about correcting errors in a surface code, intended to be used in topological quantum computing.

You are presented with a grid, representing qubits on a torus. From time to time, a syndrome measurement is made and you have to correct the errors. Now, we know how to correct errors in a quantum error correction code, but the idea is to optimize the order in which multiple errors are corrected so that the logical qubits will survive as long as possible. In a toroidal code that means that you do not want an error syndrome that stretches from one end of the grid to the other. The data from this game will be used to optimize the order of error correction in actual algorithms in some way, but, as I said, I have not seen a technical discussion of this yet.

The Game:

The game is a puzzle game involving combining numbers, in some ways similar to the viral hit 2048. From time to time, numbers in different colors will appear on a grid. You can combine to numbers of the same color that are next to each other and they will add together forming a single number. When they reach a multiple of ten they disappear. The objective is to keep going for as long as possible until you get a string of numbers that goes from one edge of the grid to another.

If you were a 2048 addict, you will probably find this game only marginally less addictive (the lack of sliding blocks is slightly less satisfying). You really do not need to know the quantum mechanics behind the puzzle, and, unlike in Quantum Moves, I doubt it will help you. You just need to know how numbers add to multiples of ten. I can see myself playing this game in the same sorts of situations I played 2048, i.e. when I have five or ten minutes of waiting time so it is not worth starting something that would take a long time. I feel a bit better about playing Decodoku than 2048, knowing that it could actually contribute to science in some way.

The graphics look like they were programmed on a Commodore 64 in the 1980’s. I assume that is because James is not a professional game developer rather than being deliberately retro, but in any case, graphics are not a major factor in the playability of this kind of game.

**Top Pick for Education: Quantum Game with Photons**

Platform: Web

Project Lead: Piotr Migdal (Freelance)

Science: 8

Gameplay: 8

Graphics and sound: 8

The Science:

This game is about linear optics, and it basically explores what you can do with photons on an optical table. You can place objects like beamsplitters, mirrors, etc. on a grid, then fire the lasers and see which detectors fire.

The idea of this is to allow people to play around with quantum optics freestyle, as well as solving puzzles. Most of the puzzles involve single-photon interference, although there is some entanglement on later levels.

I think that introducing quantum theory via photon interferometry is a great idea, as it allows you to get to the mathematics of a qubit quickly for students who have studied some classical optics. I can see myself using this game in sandbox mode as a demonstration tool in the classroom, as well as having the students solve some of the puzzles.

The Game:

You can play the game in a sandbox mode, or solve a series of puzzles where certain elements are fixed and you have to place a limited number of other elements to get certain detectors to click. Many of these puzzles are based on well-known experiments like the Mach-Zehnder interferometer or the Elitzur-Vaidman bomb. However, some of them are challenging even for a physicist experienced in the theory of weird and wonderful interferometers, e.g. they involve putting beamsplitters in unusual places that you would not immediately think of. The learning curve is well-judged and the game is fun to play, at least if you are someone who already likes to think about physics. I don’t know how well it would do as a tool for drawing people into physics.

This game is browser based and the web design is very slick and pretty. The game board itself is just a minimalist white grid, with symbols for the various elements. It could be prettier, but it is perfectly functional.

**Top Pick for Outreach: The BIG Bell Test**

Platform: Web

Project Lead: Morgan Mitchell (ICFO, Barcelona)

Science: 8

Gameplay: 7

Graphics and sound: 10

The Science:

On November 30, 2016, several labs around the world participated in the BIG Bell Test, which aimed to close the free will loophole in Bell’s theorem by using randomness generated by human “free will” to choose the measurement settings. Now, if you believe that human choice is genuinely free, and uncorrelated with anything else in the universe, then this really does close a relatively minor loophole in Bell’s theorem. On the other hand, there is reason to doubt that genuine free will exists, and there are also other ways of getting the same sort of loophole, such as retrocausality (the future affects the past) that this experiment does not address.

However, the BIG Bell Test was great for outreach, as the website, games, and videos were very slickly done and it did genuinely make you feel like you were contributing to science in a fun and simple way. It probably introduced Bell’s theorem to many people who would not have known about it otherwise.

The Game:

You can still play the BIG Bell Test games online, although there is little point as the experiments are now over. The basic idea is to get participants to mash on the 0 and 1 keys in order to extract random numbers to be used in the experiments. On the face of it, this task would be pretty boring, and we know that humans are not very good at generating random sequences anyway, so the game has to address these two issues.

To address the boredom issue, the generation process is divided into a number of short subgames that have different themes. For example, in the first game your randomness propels you forward along a road in a village, and you have to collect atoms along the way. In the second game, an oracle attempts to predict which key you will press next, and your objective is to outsmart the oracle by being unpredictable.

To address the randomness issue, some statistical tests are run in the background. The player is given feedback on how well they are doing, and is encouraged to be “more random” if necessary. You are scored on each game based on how random you are, and there is a target level of randomness to achieve in each game. I am not sure how all this works on the mathematical level. I presume the game is not computing Kolmogorov complexity, as this is uncomputable in general, but rather some simpler statistical tests that have been found to work well in practice. I also assume that randomness extraction is run on the resulting data. In any case, on November 30, at the end of the game you were told how many bits of randomness you generated, and in which lab they were used, which is a nice touch.

One of the most compelling aspects of the game is the visuals, which are done in a monochrome style that looks hand-drawn and cartoon-like. This really helps to draw the player in, as you want to see what graphics are coming up in the next game. The only complaint I have is that the 0’s and 1’s that you generate are represented by halves of a yin-yang symbol. To put it bluntly, to me, these look like sperm. For me, this just added to the quirky charm of the graphics, but I imagine it might be distracting for some players.

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]]>Vice Chair Candidates: Jay Gambetta and Susan Coppersmith

Member at Large Candidates: Stephanie Wehner and Ryan Babbush

Listed below is a statement from each candidate.

**Jay Gambetta (Candidate for Vice Chair)**

Quantum information science is the area of science that blurs standard boundaries and pushes us to understand nature at its most fundamental level. It brings together scientists from virtually all scientific disciplines to collectively try and understand the depths of fundamental physics and information theory for explaining aspects of the natural world around us. We research fundamental questions related to how physics and information theory are intertwined, to how nature computes, and to the foundations of the world around us. One would be hard-pressed to find any other division in the APS that covers such a broad and rich area, and I am very excited to run for Vice Chair of the executive committee of the Topical Group of Quantum Information (GQI).

Quantum, as ubiquitous in popular science as the word has become, is a pre-eminent pillar of physics and the beauty of quantum information science is its diverse and powerful nature. On one day a researcher could be working on foundations of physics and on the following day be considering applications of a new model of computation. The breadth of our research field is one of the many reasons why we are on the path to becoming a division of the APS. The evolution and growth of our field of quantum information has accelerated in recent years, as is clearly evident when I look back at my own personal journey starting from foundational research on open quantum systems to working closely with experimentalists on demonstrating concepts of quantum information processing.

It is a very exciting time for our community as we have recently met the requirements for becoming a division of the APS and last year, thanks to the generous support of IBM, we have our own award – **Rolf Landauer and Charles H. Bennett Award in Quantum Computing**– which recognizes the great work of our community. My goals for the GQI are 1) to continue the excellent work of the executive committee before me and to make sure we remain a division through increasing membership, 2) to encourage and develop more recognition for the younger researchers in quantum information – we need more awards and diversity for them, and 3) to increase the visibility of quantum information science in the public sphere. This is an area that is very important to me personally as in recent years I have been deeply involved in creating the IBM Quantum Experience, which is a substantial collaborative effort with colleagues that provides free public access to a fully-functioning small quantum computer. We have over 30K users learning about quantum information science as well as a large number of researchers using the Experience as a world class research tool to help produce research papers and further our understanding of nature.

In the past, I have served the GQI by chairing for the last two years the APS Fellowship committee where we have been very successful and had 11 top researchers accepted as GQI-sponsored APS fellows. As a topical group, we don’t have a final say in the selection of our Fellows since they are voted on by the governing division. To have such a large number be accepted for APS fellowship points to the top-class research being performed and the subsequent recognition of our researchers by the broader physics community.

**Susan Coppersmith (Candidate for Vice Chair)**

It is a tremendously exciting time for the field of quantum information. The APS Topical Group on Quantum Information (GQI) is important for the field not only for its role in facilitating communication between quantum information researchers, but also because of its role in communicating the great intellectual challenges and achievements of the field to other physicists as well as the general public.

I am honored to be a candidate to serve GQI as Vice-Chair. If elected, I will strive to make the organization as fair and efficient as possible, I will work to increase the diversity of the membership to maintain a membership sufficient for Division status, and I will also work hard to enhance the appreciation of quantum information in the broader community of physicists and in society at large.

Dr. Susan Coppersmith is a theoretical physicist who has been working in the field of quantum information science since 2001. She is currently a Professor of Physics at the University of Wisconsin-Madison. Her Ph.D. in physics is from Cornell University, and she has been a postdoc at Brookhaven National Laboratory and at AT&T Bell Laboratories, a visiting lecturer at Princeton University, a member of technical staff at AT&T Bell Laboratories, and a professor at the University of Chicago. She has been working to develop qubits using quantum dots in silicon/silicon-germanium heterostructures, and has also investigated the properties of algorithms involving single- and multi-particle quantum random walks.

Dr. Coppersmith has served as Chair of the UW-Madison physics department, as a member of the NORDITA advisory board, as a member of the Mathematical and Physical Science Advisory Committee of the National Science Foundation, and as a Trustee at the Aspen Center for Physics. She has served as Chair of the Division of Condensed Matter Physics and of the Group for Statistical and Nonlinear Physics of the American Physical Society, as Chair of the Division on Physics of the American Association for the Advancement of Science, as Chair of the Board of Trustees of the Gordon Research Conferences, and as Chair of the External Advisory Board of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. She is a fellow of the American Physical Society, the American Association for the Advancement of Science, and the American Academy of Arts and Sciences, and has been elected to membership in the National Academy of Sciences.

**Stephanie Wehner (Candidate for Member at Large)**

I have never been as excited about quantum information as in the past three years. On the one hand, quantum information is proving its worth to understand fundamental aspects of nature; the term “it from bit” capturing the idea, or maybe rather the dream, that all of nature could be deciphered using the perspective of information processing.

On the other hand, we are at last edging close to seeing quantum computing technologies being realized by most impressive experimental efforts. Recent years have seen a paradigm shift in the field, marked by the commitment of several large companies such as Intel, Microsoft, and Google as well as international efforts such as the EU Flagship on quantum technologies.

I believe quantum information has always drawn great strength from interdisciplinary collaboration. It is now time to fulfill the promise of quantum computing and communication technologies – if possible. However, without joint efforts from both theoretical and experimental physics, computer science, and mathematics we cannot succeed. The recent paradigm shift also sees a necessary expansion into the domain of engineering, and I believe we will see a new field of applied quantum computer science emerge which in analogy to most of classical computer science employs a heuristic approach to realize and utilize quantum technologies.

GQI now has the potential to bring the old and new communities in quantum information together. I will contribute to GQI stepping up to a Division in order to realize this goal. Recent developments also highlight new career opportunities for junior researchers to enter or indeed found quantum industry. I would like GQI to help facilitate such opportunities and navigate challenges.

I am honored to be a candidate for the GQI member-at-large. Due to my own interdisciplinary background, my collaborations across disciplines with both theory and experiment, as well as my international experience in the US, Asia and Europe I believe I am well positioned to represent the diverse GQI community. I enjoyed making a difference by founding QCRYPT and advancing QuTech Academy, and I would now be excited to serve in the APS to take GQI forward.

Stephanie Wehner is an Antoni van Leeuwenhoek Professor at QuTech, Delft University of Technology in the Netherlands. She received her PhD degree in computer science from the University of Amsterdam in 2008, followed by two years as a Postdoctoral Scholar at the California Institute of Technology. From 2010-2014 she was an Assistant Professor and later Dean’s Chair Associate Professor at the Centre for Quantum Technologies, National University of Singapore. Prior to her academic career, Stephanie has worked for a few years in the network security industry as a professional hacker.

Stephanie’s passion is the theory of quantum information in all its facets, and she has published more than 60 articles on a wide range of topics in physics and computer science, ranging from more applied subjects such as (quantum) information theory and quantum cryptography to fundamental questions in quantum foundations and quantum thermodynamics. Some of her contributions to scientific progress have been selected for Science’s “Top 10 Breakthroughs of 2015”, and Nature’s “Science Events that shaped 2015”, and received the Paul Ehrenfest Award for Quantum Foundations. Stephanie was awarded personal grants including the ERC Starting Grant.

Stephanie is one of the founders of QCRYPT, which has grown to be the largest international conference in quantum cryptography. She has served on the steering committees of several conferences, QCRYPT 2011-2016, QIP 2014-2016, and QCMC 2015-2017, as well as on the editorial board of the New Journal of Physics. She has organized several international conferences such as QCRYPT, QIP and workshops such as the IMS workshop on Quantum Thermodynamics. At QuTech, she is part of the management team, as well as responsible for QuTech Academy, an interdisciplinary education program in quantum technologies for students in engineering, physics, computer science and mathematics. She enjoys spreading the word about quantum information, for example by teaching online in edX QuCryptoX, and contributing to outreach by speaking at events such as TEDx and New Scientist Live.

**Ryan Babbush (Candidate for Member at Large)**

Five years ago, a wise postdoc sat me down for a serious conversation; they urged me to abandon quantum information while I still could because there were no jobs and the field seemed doomed. Fortunately, we both ignored that advice and today, laugh about that discussion. The size and number of industrial quantum groups is growing, funding for academic researchers and government programs is increasing, as is the size and quality of quantum hardware. Now is an extremely exciting time for the field.

However, now is also an uncertain time for the future of science in the United States. Michael Lubell, director of public affairs for the APS, told Nature that “Trump will be the first anti-science president we have ever had. The consequences are going to be very, very severe”. Whether one agrees with this sentiment or not, with both executive and legislative branches under Republican control, the incoming administration will have tremendous power to reshape science policy in America. How policy changes will affect quantum research is unclear and quite possibly, still undecided by lawmakers. In my view, how the APS will represent our interests to these lawmakers in 2017 is the most important issue in the current APS election.

If I am elected Member-at-Large of GQI, I will use my position on the GQI committee to advocate for increased lobbying on behalf of our group’s interests. As a representative of the APS and an American citizen, I will participate in all APS lobbying efforts and personally travel to DC to meet with congressional staffers about the importance of supporting quantum research. I will wear a tie and tell anyone willing to listen that academic and government research in quantum information is essential for the development of future technology and also creates industry jobs (such as mine). I will tell them that America’s competitive advantage in this field demands the availability of visas for the best physicists to work here, regardless of their nationality. But most importantly, I will tell them about the promise of quantum information and remind them that leadership in science is part of what makes America great.

Ryan Babbush is a Research Scientist in the Quantum AI Lab at Google where he works closely with experimentalists to design quantum algorithms for prototype quantum hardware. He has broad interests in quantum algorithms, quantum complexity, machine learning, superconducting qubits, chemical physics and electronic structure theory.

Ryan entered undergraduate studies intending to become a chemist. However, after two years of research in experimental chemistry and two trips to the hospital for toxic exposure in the laboratory, Ryan decided it was safer to be a theorist. As he quickly learned, most chemistry is just physics that’s too hard for physicists… unless the physicist has a quantum computer, in which case most chemistry is just a problem in the quantum complexity class BQP. This realization convinced Ryan to enter the field of quantum information. He graduated from Carleton College with a double major in Physics and Chemistry (2011) and headed to Harvard University where he joined the Aspuru-Guzik group, known for working at the intersection of quantum information and quantum chemistry. Ryan received both his masters in Physics (2013) and his PhD in Chemical Physics (2015) from Harvard University.

At Harvard and Google Ryan worked on developing efficient analog and digital protocols for quantum computing problems in chemistry and machine learning. He has collaborated with experimental groups using ion traps, NV centers, and several types of superconducting qubits to realize these algorithms. During his PhD he did internships with quantum groups at both Google and Microsoft. Upon disserting in 2015, he joined Google’s team as a permanent researcher.

]]>The book begins by postulating a peculiar telephone. Alice and Bob–the heroes of many a paper on quantum information–each have a telephone, which is useless for communication: it produces only random noise. But they discover that the noise produced on the two sides is perfectly synchronized. Being good scientists, they try to determine whether the correlations arise due to communication from one side to the other, or due to some common cause, such as a long random sequence stored identically in each telephone before they were distributed.

From this science fictional scenario we are led to the idea of a Bell experiment: two widely separated experimenters, each equipped with a black box that has two settings and two possible outputs. Gisin lays out the description of a Bell game (actually, the CHSH game), and derives the CHSH inequality that must be satisfied if the two black boxes cannot communicate, but are correlated due to a common cause. He then describes how such a Bell test can be carried out in an actual quantum experiment, and how quantum mechanics predicts that the inequality is violated. This, in the language commonly used in quantum theory, is *quantum nonlocality*.

From there he presents related concepts from the heart of quantum information: the no-cloning theorem and entanglement. He describes how real world experiments have been designed to test Bell’s theorem, and how all tests to date have supported the predictions of quantum mechanics. He discusses the two major loopholes in experimental Bell tests, the locality and detection loopholes. (This book was written before the three loophole-free Bell experiments done in 2015. Perhaps he will add them to a future edition, since Gisin himself is a major contributor to the study of such loopholes.) He describes his 2008 experiment, which showed that any hidden superluminal communication between the two sides must be many times faster than the speed of light.

There are, of course, philosophical loopholes that are probably impossible to close, such as *superdeterminism*: the idea that all of Alice and Bob’s choices, as well as the seemingly random outcomes are determined from the beginning of the universe. Gisin briefly discusses a number of related topics, like the *Free Will Theorem* of Conway and Kochen, and outlines his more recent result (with collaborators Bancal et al.) that proves a remarkable extension of Bell’s theorem. Using 3- and 4-body correlations, they show that if correlations arise from influences propagating at any finite velocity, they must eventually either disagree with the predictions of quantum mechanics or allow superluminal communication (or both).

In addition to its central focus on Bell experiments and nonlocality, the book also discusses some applications of entanglement. There are two fairly brief chapters, one on random number generators and quantum cryptography and one on quantum teleportation, which hint at the large effort now being devoted to quantum-based technology.

The philosophical heart of the book, to which the author repeatedly returns, is this: if quantum mechanics violates Bell inequalities, then the randomness of quantum measurements is *not* due to ignorance, like the seeming randomness of a tossed coin or of thrown dice. Rather, it must be *true randomness*: new information that spontaneously appears out of nowhere. Gisin argues that because of its nonlocality, quantum mechanics is inconsistent with a deterministic, Newtonian world view. This argument–like all arguments in quantum foundations–has been disputed, but I have never seen it presented with such cogency as in this book.

While “Quantum Chance” does not assume knowledge of quantum mechanics, and derives all its arguments from first principles, it will not be an easy read for most laypeople. Several early chapters bristle with equations and tables, and the book draws on some math (like binary arithmetic and probability theory) that might be daunting to a mathematically unsophisticated reader. However, it is easily readable by technical readers who are not specialists in quantum theory. They will find it a concise and highly accessible introduction to Bell’s theorem, and to the ideas of entanglement and quantum nonlocality. And specialists will find it interesting as well, as clearly presenting the ideas of one of our deep thinkers about quantum theory.

]]>As usual, if you are watching with a group and want to reserve a seat in the hangout then leave a comment on the event page:

https://plus.google.com/events/cbf9m2hsuf9kgvv3p61alo7h7lc

We also encourage individuals interested in active participation—which typically involves asking questions after the talk—to join the hangout. Otherwise you can watch on the livestream. Details follow.

Title: Size-driven quantum phase transitions

Speaker: David Perez-Garcia, Universidad Complutense de Madrid

Abstract: Most of the theoretical knowledge about quantum many body systems comes from performing numerical simulations. One tries to capture the relevant physical features of a system by extrapolating to the large system size the knowledge obtained in the analysis of an increasing sequence of finite-size systems, which must be small enough for the computer to be capable of giving an answer in a reasonable amount of time. In this work we show simple examples that totally defeat any such approach. More concretely, we construct translationally invariant quantum spin models on the 2D square lattice with reasonably small local dimension exhibiting the following surprising feature that we refer to as a “size-driven phase transition”‘: For all system sizes smaller than a threshold value L, the system has a unique ground state with product structure and a constant spectral gap to the first excited state, which also has product structure. However, for all system sizes larger than L, the system has topological quantum order, meaning a finite number of ground states which are locally indistinguishable, a finite spectral gap and first excited states with anyonic statistics. Moreover, we construct examples (all of them with local dimension smaller than 10) for which the threshold size L can occur at essentially any order of magnitude. From sizes that are reachable within current experimental setups and numerical simulations (L=15 or L=84) to sizes that are beyond any present or future capability, such as L> 10^35000.

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