Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session A21: Machine Learning for Quantum Matter IFocus Live

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Sponsoring Units: DCOMP GDS DMP Chair: Stefanie Czischek, University of Waterloo 
Monday, March 15, 2021 8:00AM  8:36AM 
A21.00001: Dynamics in correlated quantum matter with neural networks Invited Speaker: Markus Heyl The efficient numerical simulation of nonequilibrium realtime evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this talk I will present a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum manybody wave functions. We identify and resolve some key challenges for the simulation of time evolution, which previously imposed significant limitations on the accurate description of large systems and longtime dynamics. As a concrete example, we study the dynamics of the paradigmatic twodimensional transverse field Ising model, as recently also realized experimentally in systems of Rydberg atoms. Calculating the nonequilibrium realtime evolution across a broad range of parameters, we, for instance, observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached time scales are comparable to or exceed the capabilities of stateoftheart tensor network methods. 
Monday, March 15, 2021 8:36AM  8:48AM Live 
A21.00002: Neural network enhanced hybrid quantum manybody dynamics Rouven Koch, Jose Lado Computing dynamical properties in quantum manybody systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in realtime and frequency space, computational limitations often dramatically constrain the physical regimes in which quantum many body dynamics can be solved. Here we show [1] that the combination of machine learning methods and complementary manybody tensor network techniques substantially decreases the computational cost of quantum manybody dynamics. We demonstrate that combining kernel polynomial techniques [2] and realtime evolution, together with deep neural networks, allows to compute dynamical quantities faithfully. We show that this hybrid neuralnetwork manybody algorithm can efficiently extrapolate dynamics in the presence of numerical noise, learning to detect defective data and correcting it. Ultimately, our results provide a starting point towards adversarial neuralnetwork algorithms for predicting quantum manybody dynamics that could potentially solve computationally expensive manybody systems in a more efficient manner. 
Monday, March 15, 2021 8:48AM  9:00AM 
A21.00003: Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation Di Luo, Zhuo Chen, Juan Carrasquilla, Bryan Clark The theory of open quantum systems is crucial for quantum science and engineering. Simulations of such systems are computationally expensive due to the exponential growth of the extended Hilbert spaces' dimensionality. We propose an efficient machine learning approach to simulate such dynamics using a probabilistic formulation of quantum mechanics based on the positive operatorvalued measure, parameterizing the quantum states with autoregressive neural networks for exact sampling. In addition, we use the String States to improve local correlations and partially restore symmetries. We solve for the dynamics using the forwardbackward trapezoid method and for the steadystate solution variationally. We benchmark our algorithms on one and twodimensional systems. The results are significantly more accurate than other approaches using restricted Boltzmann machines with Markov chain Monte Carlo sampling. This work shows an efficient approach to solve quantum dynamics as well as highdimensional probabilistic differential equations, which provides a general method to understand both quantum and classical phenomena in various contexts. 
Monday, March 15, 2021 9:00AM  9:12AM Live 
A21.00004: Customizable neuralnetwork states for topological phases Agnes Valenti, Eliska Greplova, Netanel Lindner, Sebastian Huber Obtaining an accurate ground state wave function is a key question in the quantum manybody problem. Variational methods have proven to be excellent computationally scalable tools for the efficient approximation of ground states. Recently, generic tools such as neural networks have been established as versatile ground state ansatzes. Here, we introduce an interpretable physically motivated variational neural network ansatz based on a tunable extension of the Restricted Boltzmann Machine architecture. We illustrate its success on the example of Kitaev's toric code in the presence of magnetic fields and the transverse field Ising model. We are able to identify critical perturbation strengths leading to a transition out of the topological phase of the toric code model whose first or second order nature depends on the direction of the magnetic fields. The flexibility of our variational ansatz allows us in addition to study more subtle properties of the phase diagram, such as firstorder transition lines outside of the topological phase. We achieve this by formulating a novel algorithm for identification of excited states in the framework of variational Monte Carlo. 
Monday, March 15, 2021 9:12AM  9:48AM Live 
A21.00005: Variational Neural Annealing Invited Speaker: Mohamed HibatAllah Many combinatorial optimization problems relevant to computer science, computational biology, and physics can be tackled with simulated annealing, which is a powerful framework for optimizing the properties of complex systems through the lens of statistical mechanics. However, simulated annealing and its quantum counterpart, simulated quantum annealing, are traditionally implemented via Markov chain Monte Carlo, often displaying slow convergence to optimal solutions for challenging optimization problems. In this talk, we present a combination of the variational principle in classical and quantum physics with recurrent neural networks (RNNs), whose dynamics are naturally devoid of slow Markov chains, to accurately emulate annealing in its classical and quantum formulations, for the purpose of solving optimization problems. We find that our variational implementation of classical annealing is not only superior to its quantum analog in terms of speed of convergence and accuracy of solutions but also outperforms traditional simulated annealing and simulated quantum annealing on prototypical spin glass models. These results advocate for the use of our variational implementation of classical annealing as a competitive algorithm to tackle realworld optimization problems. 
Monday, March 15, 2021 9:48AM  10:00AM Live 
A21.00006: A NeuralNetwork approach to the simulation of Open Quantum Dynamics using POVMs Moritz Reh, Martin Gaerttner, Markus Schmitt Artificial Neural Networks (ANNs) have proven to be powerful function approximators in many realms of physics. Among many other achievements, they present a competetive approach to the solution of the quantum manybody problem, utilizing state of the art networkdesigns that represent inherent physical properties of the system under scrutiny, e.g. translational symmetry in Convolutional Networks. While promising results have been obtained for the time evolution in the case of closed quantum systems in which the ANN serves as a variational wave function, the more general case of the dynamics of open quantum systems has not received as much attention. We encode the density matrix by its corresponding POVM probability distribution. This distribution is represented through the parameters of an ANN for which we explicitly construct updates corresponding to dissipative Lindbladian dynamics. This is achieved using a Time Dependent Variational Principle. Different network architectures are explored and compared. 
Monday, March 15, 2021 10:00AM  10:12AM Live 
A21.00007: Hamiltonian reconstruction as metric for a variational study of the spin1/2 J_{1}J_{2} Heisenberg model Kevin Zhang, Samuel Lederer, Kenny Jing Hui Choo, Titus Neupert, Giuseppe Carleo, EunAh Kim Evaluating the quality of variational wavefunctions is a hard task due to the large dimensionality of Hilbert space. At the same time, modern methods such as artificial neural networks or variational quantum eigensolvers need accurate evaluation of wavefunctions to facilitate effective development. We propose using a recently developed Hamiltonian reconstruction method for a multifaceted approach to evaluating wavefunctions. Starting from convolutional neural network and restricted Boltzmann machine ansatze trained on a square lattice spin1/2 J_{1}J_{2} Heisenberg model, we compare reconstructed Hamiltonians to the original Hamiltonian to evaluate various aspects of the wavefunction. The reconstructed Hamiltonians are systematically 1) less frustrated, and 2) have easyaxis anisotropy near the high frustration point. Also, in the large J_{2} limit, furtherrange interactions are induced in the reconstructions. This highlights the importance of implementing symmetries explicitly in neural network ansatze. 
Monday, March 15, 2021 10:12AM  10:24AM Live 
A21.00008: Convolutional Neural Network Wave Functions: learning quantum manybody physics Douglas Hendry, Adrian Feiguin Convolutional neural networks (CNN) have become a staple of modern machine learning research, since they are ideally suited for applications with spatial and/or temporal features such as images, videos, and signals. The key feature of CNNs is their internal structure which is designed to prioritize local features and produce a result that it translational invariant. This has made them an ideal candidate for variational wave functions (VWF) to represent ground states of quantum manybody 2D systems. However, achieving results that improve on existing computational methods has been challenging, mainly due the difficulty of augmenting existing CNN architectures and training them. Here, we propose, discuss and benchmark novel strategies to improve and train CNNs as VWF for the frustrated 2D J1J2 Heisenberg model on the square lattice with focus on the use of real or complex weights, choice of activation functions, the overall architecture, and enforcement of symmetries. 
Monday, March 15, 2021 10:24AM  10:36AM Live 
A21.00009: Challenges for simulating quantum spin dynamics in two dimensions by neural network quantum states Damian Hofmann, Giammarco Fabiani, Johan H Mentink, Giuseppe Carleo, Michael Sentef Neuralnetwork quantum states are a versatile ansatz for the representation of quantum states and in particular have shown promise for highly entangled ground states in twodimensional spin systems. They have also been successfully applied to simulating dynamics by propagation with timedependent variational Monte Carlo (tVMC) [14], which is a stochastic version of the timedependent variational principle (TDVP). However, there are a number of open challenges on the way to achieving stable time propagation for a wider range of systems and excitations [2,5,6]. 
Monday, March 15, 2021 10:36AM  10:48AM Live 
A21.00010: Gauge equivariant neural networks for quantum lattice gauge theories Di Luo, Giuseppe Carleo, Bryan Clark, James Stokes Gauge symmetry plays a fundamental role in physics. We propose a family of neuralnetwork quantum states with gauge equivariant architecture which exactly satisfy the local Hilbertspace constraints of quantum lattice gauge theories. It is shown that the gauge equivariant neural network has exact represention of the ground state solutions for Zn Toric code model corresponding to the loopgas solution. For Z2 Toric code model with transverse field away from the exactly solvable limit, we apply the gauge equivariant neuralnetwork quantum states as trial wavefunctions within variational quantum Monte Carlo to obtain compact descriptions of the ground state and understand the phase transition. 
Monday, March 15, 2021 10:48AM  11:00AM On Demand 
A21.00011: Quantum Ground States from Reinforcement Learning Ariel Barr, Willem Gispen, Austen Lamacraft The past few years have seen numerous attempts to leverage the power of deep networks to solve the quantum manybody problem, and neural representations of many body wavefunctions have proliferated. However, there are several mathematically equivalent formulations of quantum mechanics, and hence alternative routes for the application of machine learning. 
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