View from the arXiv: Jun 27 - Jul 1 2022

Welcome to ‘View from the arXiv’, where each week I’ll put together a short list of new preprints which have appeared on arxiv.org during the week which I’ve found interesting. I’ll focus on the categories ‘Disordered Systems and Neural Networks’, ‘Quantum Gases’ and ‘Strongly Correlated Electrons’, and in particular the first two as these are the main areas of the arXiv which I follow. This is an entirely subjective list of things which appeal to me, and of course there are far too many interesting papers to be able cover all of them so I just choose one or two from each day to highlight here. As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details. (And let’s face it, this caveat should be applied to any published work too…!)

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June 27th

Spatially programmable spin interactions in neutral atom arrays, by Lea-Marina Steinert, Philip Osterholz, Robin Eberhard, Lorenzo Festa, Nikolaus Lorenz, Zaijun Chen, Arno Trautmann, and Christian Gross: Analog quantum simulators, as they are now known, are experimental platforms that directly implement a mathematical model of interest on real atoms and allow experimenters to measure the desired properties. This is a powerful, efficient approach to studying quantum systems, but it’s not particularly flexible. Not all models can be implemented experimentally, and engineering even the simplest mathematical model is a huge experimental challenge. This paper reports on new work making analog quantum simulators more flexible by allowing arrays of Rydberg atoms with highly flexible interactions, which enables experimenters to study more complex mathematical models than they were previously able to. Further work building along these lines might even enable a fully programmable analog quantum simulator, capable of simulating almost anything that we might want to! This paper contains a lot of experimental details that are a bit over my head, but it looks like an impressive technical achievement and a very nice step forward in the capabilities of these experimental platforms.

June 28th

Confinement Induced Frustration in a One-Dimensional ℤ2 Lattice Gauge Theory, by Matjaž Kebrič, Umberto Borla, Ulrich Schollwöck, Sergej Moroz, Luca Barbiero, and Fabian Grusdt: Quantum simulation has made huge progress in recent years, and the recent development of quantum simulators capable of realising lattice gauge theories is an exciting step. This work takes previous studies one step further - and closer to a realm that I’m familiar with - by adding frustration into the mix, and studying a lattice gauge theory where the nearest-neighbour repulsion between particles and the gauge-mediated confining field each have opposite effects (i.e. one pushing particles apart, and the other pushing them together), which gives rise to some complex behaviour with some very intriguing underlying physics. The authors map out a phase diagram and suggest some observables that might be experimentally measurable, so we could see real experiments investigating this model in the very near future, which would be quite exciting.

Quantum transport of strongly interacting fermions in one dimension at far-out-of-equilibrium, by Jie Zou, and Xiaopeng Li: It’s always interesting to see new techniques for the study of quantum systems far from equilibrium, and this work studies a widely-used model (the XXZ spin chain) in the strongly interacting limit using a method that maps the interacting (i.e. hard) problem onto an equivalent non-interacting (i.e. much easier) problem, enabling the authors to study extremely large systems and long timescales without running into the sort of difficulties that might be encountered by other numerical methods. The details of the method are contained in other papers – though I would have liked to have seen a little more information on them given here, as it’s hard to judge the limitations of the method from this paper alone – but the results are extremely interesting.

Cracking nuts with a sledgehammer: when modern graph neural networks do worse than classical greedy algorithms, by Maria Chiara Angelini, and Federico Ricci-Tersenghi: This might be my favourite paper of the week, and though it’s not a topic I know much about, I felt that I just had to include it here. This paper is a response to a recent paper which claimed that graph neural networks are superior than other methods when applied to a certain class of problems. This work shows that these claims are not justified, and that in fact a much simpler algorithm can solve these problems much faster (by 4 orders of magnitude!), despite being older and less flashy. The key point here isn’t that the other paper is wrong per se, but that many claims of the superiority of neural networks and other deep learning techniques are being made without sufficient rigour, as there’s no standardised way of benchmarking these techniques. The authors propose a problem that could serve as a standard benchmark, though I suspect it will take the field some time before a comprehensive set of benchmarks and tests is found that all future optimisation methods can be tested to better understand just what sorts of problems they are best at.

June 29th

Exact Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants, by Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, and Pedro Ribeiro: Quasi-periodic systems offer an interesting intermediate scenario between fully random disordered systems on the one hand, and entirely clean translationally invariant systems on the other. They are described by an on-site potential that varies in a deterministic yet non-periodic way, giving rise to a kind of ‘controlled non-random disorder’ that leads to many unusual properties not shared by random systems. This work constructs a renormalisation group approach to studying generic quasiperiodic systems in one dimension, which is able to capture the metallic, localised and critical phases of the model. If I understand rightly, it’s limited to non-interacting systems at the moment, but I’ll be watching with interest to see if this can be generalised to include interactions, as this could be a very interesting method for the study of many-body localisation in quasiperiodic models!

How quantum phases on cylinders approach the 2d limit, by Yuval Gannot, and Steven A. Kivelson: There are by now many ways to efficiently simulate one-dimensional quantum systems, but comparatively few ways to numerically investigate two-dimensional quantum systems. The sheer increase in complexity caused by an additional dimension makes this problem incredibly difficult. One way around this is to consider coupling one-dimensional systems together, starting with two one-dimensional chains that are linked to form a ladder-like structure, then adding a third, a fourth, and so on until the two-dimensional limit is reached. This paper considers a similar setup, but here with one-dimensional chains arranged in a cylindrical geometry: as the circumference of the cylinder is increased, the system becomes more and more two-dimensional. This analysis is based on an earlier work, and is only valid assuming that the two-dimensional system is a superconductor, but it nonetheless shows that valuable information about the two-dimensional system can be gained by simulating quasi-one-dimensional models on cylindrical geometries, validating numerical studies that use this approach and providing further information about how trustworthy these sorts of studies are and what they are accurately able to conclude.

Anomalous Floquet-Anderson Insulator with Quasiperiodic Temporal Noise, by Peng Peng Zheng, Christopher I. Timms, and Michael H. Kolodrubetz: It’s been known for a while now that interesting physics can arise from even relatively simple models when you apply periodic temporal drive (i.e. you shake the system in a periodic way). This paper considers a phase known as an anomalous Floquet Anderson insulator (AFAI), subject not to time-periodic noise, but quasiperiodic noise. Similar to the quasiperiodic disorder we looked at above, this is an intermediate case between perfectly periodic drive (known as Floquet drive) and totally random noise (e.g. white noise). This allows researchers to probe how the AFAI phase breaks down as the drive becomes more noisy, allowing them to investigate how stable the phase is to imperfect drive protocols. This ultimately leads to a theoretical model which is Anderson localised in one dimension, and Wannier-Stark localised in another, which is an interesting unsolved problem and something I’d be very curious to see future work look at.

June 30th

Numerical simulation of non-abelian anyons, by Nico Kirchner, Adam Smith, and Frank Pollmann: I’ve mentioned in a previous entry this week that numerically simulating two-dimensional systems is a tricky challenge, but there are some physical effects that only happen in two dimensions, and so it’s crucial to develop approaches able to study these. One particular example is given in this paper, that of a type of particle called a ’non-Abelian anyon’ which is a type of composite particle (quasiparticle) that obeys neither fermionic nor bosonic exchange statistics. This paper presents a scheme to numerically simulate the non-equilibrium dynamics of anyons in two-dimensional systems, and computes various quantities such as the level spacing statistics and the non-equilibrium dynamics following a quench, for three different types of anyon. As the authors say, this paper is just a first demonstration of their algorithm, and it’ll be very interesting to see where they go from here.

Ultracold ion-atom experiments: cooling, chemistry, and quantum effects,, by Rianne S. Lous, and Rene Gerritsma: I’ve often talked in these pages about ultracold atoms and trapped ions, but the idea of combining both types of experimental platform is new to me! This review article covers just that: the interplay between a small number of trapped ions immersed in an ultracold atomic gas. I’ll say no more about it and simply suggest that you read the review article if you’re interested - this is an experimental setup that’s very new to me and something that looks incredibly exciting with a lot of future potential for both experimental and theoretical work.

Optimal light cone and digital quantum simulation of interacting bosons, by Tomotaka Kuwahara, Tan Van Vu, and Keiji Saito: I have to admit, I skim-read this reasonably short paper and thought that it was pretty interesting, then just about fell out of my chair when I saw that there’s an additional >100 pages of Supplemental Material containing mathematical proofs of various things discussed in the main text. I’ll be very interested to see where this ends up published, as often the Supplemental Material isn’t even looked at by most readers, and that would be a shame for something this comprehensive. That aside however, the physics of this one is pretty interesting. Understanding how correlations and information are spread in quantum systems is a major topic in modern condensed matter and atomic physics, and while a lot of progress has been made, there are still some questions yet to be answered. This work is a very interesting stab at addressing the question of how information and correlations can spread in bosonic systems (in digital quantum simulators, crucially) via the calculation of an effective light-cone that bounds how fast information can propagate in these systems. It’s tough work, but the results are impressive.

July 1st

Neural network enhanced measurement efficiency for molecular groundstates, by Dmitri Iouchtchenko, Jérôme F. Gonthier, Alejandro Perdomo-Ortiz, and Roger G. Melko: One promising application for near-future quantum computers is the preparation of of ground states of various target Hamiltonians, and there is a lot of work going on in this field of research to determine how this can be done efficiently and accurately. This paper focuses on some particular molecular Hamiltonians, and shows that neural networks can be used to ’learn’ the ground state of a given Hamiltonian based on a set of measurement data. The authors argue that this method gives a significant improvement over classical shadow tomography, another ‘standard’ technique that’s been getting a lot of attention. The point here isn’t that neural networks alone can solve all problems, but rather that combining neural networks with other approaches in an intelligent way can lead to a hybrid method that combines the strength of both techniques, and can allow investigation of problems that would be too complicated to tackle by brute force alone.