Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session H18: Machine Learning Quantum States IIIFocus

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Sponsoring Units: DCOMP DCMP DAMOP Chair: Juan Carrasquilla, Vector Institute Room: BCEC 156B 
Tuesday, March 5, 2019 2:30PM  3:06PM 
H18.00001: Hybrid neural network  quantum simulator Invited Speaker: Giacomo Torlai The recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediatescale quantum hardware, with promising progress towards scalable quantum simulation of stronglycorrelated systems. In order to enhance the capabilities of this class of quantum devices, some of the more arduous experimental tasks can be offloaded to classical algorithms running on conventional computers. In particular, generative neural networks trained on measurement data can be implemented to obtain an approximate reconstruction of the experimental wavefunction, allowing specialized measurements which are either costly or not accessible in the experimental setup. I will present this classicalquantum hybridization for quantum hardware based on trapped ultracold atoms and superconducting qubits. 
Tuesday, March 5, 2019 3:06PM  3:18PM 
H18.00002: Reinforcement Learning Decoders for FaultTolerant Quantum Computation Ryan Sweke, Markus Kesselring, Evert Van Nieuwenburg, Jens Eisert Topological error correcting codes, and particularly the surface code, provide a promising and feasible roadmap towards largescale faulttolerant quantum computation. Obtaining fast and flexible decoding algorithms for these codes, within the experimentally relevant context of faulty syndrome measurements, is therefore an important milestone. The problem of decoding such codes, in the full faulttolerant setting, can be naturally reformulated as a process of repeated interactions between a decoding agent and a code environment. Reinforcement learning can then be used to obtain such a decoding agent, and can succesfully learn to decode in the faulttolerant setting. 
Tuesday, March 5, 2019 3:18PM  3:30PM 
H18.00003: The recoverable quantum information: A smart reward for reinforcement learning of quantum error correction Thomas Foesel, Petru Tighineanu, Talitha Weiss, Florian Marquardt Quantum information can be encoded in a complex manner in entangled multiqubit states. But how well is this information preserved, given the dissipative time evolution of a system? In order to address this question, we have developed a new quantity, which we call the recoverable quantum information. 
Tuesday, March 5, 2019 3:30PM  3:42PM 
H18.00004: Quantum error correction for the Toric code using Deep reinforcement learning Philip Andreasson, Simon Liljestrand, Joel Johansson, Mats Granath We implement a quantum error correction algorithm for the Toric code using Deep reinforcement learning. An actionvalue Qfunction encodes the discounted value of moving a defect to a neighboring site on the square grid (the action) depending on the full set of defects on the torus (the syndrome or state). The Qfunction is represented by a deep convolutional neural network. Using the translational invariance on the torus allows for viewing each defect from a central perspective which crucially simplifies the Qfunction representation independantly of the number of defect pairs. 
Tuesday, March 5, 2019 3:42PM  3:54PM 
H18.00005: Restricted Boltzmann Machines and Matrix Product States of 1D Translational Invariant Stabilizer Codes Yunqin Zheng, Huan He, Nicolas Regnault, Andrei B Bernevig We discuss the relations between the restricted Boltzmann machine (RBM) states and the matrix product states (MPS) for the ground states of 1D translational invariant stabilizer codes. A generic translational invariant and finitely connected RBM state can be expressed as an MPS, and the matrices of the resulting MPS are of rank 1. We dub such an MPS as an RBMMPS. This provides a necessary condition for exactly realizing a quantum state as an RBM state, if the quantum state can be written as an MPS. We mostly focus on generic 1D stabilizer codes having a nondegenerate ground state with periodic boundary condition. We obtain an expression for the lower bound of their MPS bond dimension, and also an upper bound for the rank of their MPS matrices. In terms of RBM, we provide an algorithm to derive the RBM for the cocycle Hamiltonians whose MPS matrices are proved to be of rank 1. Moreover, the RBMMPS produced by our algorithm has the minimal bond dimension. A family of examples is provided to explain the algorithm. 
Tuesday, March 5, 2019 3:54PM  4:06PM 
H18.00006: Neural loop algorithm for square ice model YingJer Kao, KaiWen Zhao, WenHan Kao We discuss how to apply a reinforcement learning framework on the square spin ice model. Spin ice is a frustrated magnetic system with a strong topological constraint on the lowenergy configurations called the ice rule. The conventional single spinflip Monte Carlo update breaks this constraint. We exploit a reinforcement learning method that parameterizes the transition operator with neural networks. By extending the Markov chain to a Markov decision process, the algorithm can adaptively search for a global update policy through its interactions with the physical model. We find that the global loop update emerges without the explicit knowledge of the ice rule. This method might serve a general framework to search for efficient update policies in other constrained systems. 
Tuesday, March 5, 2019 4:06PM  4:18PM 
H18.00007: Variational optimization in the AI era: supervised wavefunction optimization and computational graph states. Dmitrii Kochkov, Bryan Clark An important approach to the quantum manybody problem is to write down a compact variational ansatz which represents the target quantum state. The success of a particular model depends on its ability to capture the structure of the state and optimize all variational parameters. We introduce a machine learning inspired computational framework that works with wavefunctions represented as differentiable computational graphs and develop a novel optimization algorithm Supervised Wavefunction Optimization, that allows for effective optimization of such models. We present results on several architectures showing the efficiency of our approach. 
Tuesday, March 5, 2019 4:18PM  4:30PM 
H18.00008: Generalized Transfer Matrix States from Artificial Neural Networks Lorenzo Pastori, Raphael Kaubruegger, Jan Carl Budich We propose and investigate a new family of quantum states, coined generalized transfer matrix states (GTMS), which bridges between tensor network states and states derived from artificial neural networks (ANNs). In particular, we show by means of a constructive embedding that the class of GTMS contains generic matrix product states while at the same time being capable of capturing more longranged quantum correlations that go beyond the arealaw entanglement properties of tensor networks. While generic deep ANNs are hard to contract, meaning that the corresponding state amplitude can not be exactly evaluated, the GTMS network is shown to be analytically contractible using transfer matrix methods. With numerical simulations, we demonstrate how the GTMS network learns random matrix product states in a supervised learning scheme, and how augmenting the network by longranged couplings leads to the onset of volumelaw entanglement scaling. We argue that this capability of capturing longrange quantum correlations makes GTMS a promising candidate for the study of critical and dynamical quantum manybody systems. 
Tuesday, March 5, 2019 4:30PM  4:42PM 
H18.00009: Construction of Hamiltonians by supervised learning of energy spectra Hiroyuki Fujita, Yuya Nakagawa, Sho Sugiura, Masaki Oshikawa Handling the large number of degrees of freedom with proper approximations, namely the construction of the effective Hamiltonian is at the heart of the (condensed matter) physics. Here we propose a simple scheme of constructing Hamiltonians from a given energy spectrum [1]. The sparse nature of the physical Hamiltonians allows us to formulate this as a solvable supervised learning problem. Taking a simple model of correlated electron systems, we demonstrate the datadriven construction of its lowenergy effective model. We present potential applications for the construction of entanglement Hamiltonians and materials discovery through the construction of parent Hamiltonians from effective models of topological matters. [1]H.Fujita et.al., Phys. Rev. B 97, 075114 (2018). 
Tuesday, March 5, 2019 4:42PM  4:54PM 
H18.00010: Backflow Transformations via Neural Networks for Quantum ManyBody WaveFunctions Di Luo, Bryan Clark Obtaining an accurate ground state wave function is one of the great challenges in the quantum manybody problem. In this paper, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman, adds correlation to a meanfield ground state by transforming the singleparticle orbitals in a configurationdependent way. NNB uses a feedforward neural network to learn the optimal transformation via variational Monte Carlo. NNB directly dresses a meanfield state, can be systematically improved and directly alters the sign structure of the wavefunction. It generalizes the standard backflow[1] which we show how to explicitly represent as a NNB. We benchmark the NNB on a Hubbard model at intermediate doping finding that it significantly decreases the relative error, restores the symmetry of both observables and singleparticle orbitals, and decreases the doubleoccupancy density. 
Tuesday, March 5, 2019 4:54PM  5:06PM 
H18.00011: Contrasting the Building Blocks of Grain Boundaries using Local vs. MultiScale Universal Descriptors Derek Hensley, Conrad W Rosenbrock, Andrew H Nguyen, Gus Hart, Eric Homer The behavior and properties of Grain Boundary (GB) Systems arise from a myriad of atomistic interactions. Is it possible to describe the properties of any GB in the system using knowledge of only a few? If so, which GBs have these essential, atomistic "building blocks" from which all other GB properties can be predicted? Previously, a universal similarity metric for GBs based on the Smooth Overlap of Atomic Positions (SOAP) descriptor was shown to effectively discover the underlying physics of GBs and find these atomistic building blocks. We present another universal GB representation using a multiscale, scattering transform that also discovers GB building blocks. We contrast the building blocks discovered by SOAP with those of scattering transform to show the merits of local vs. multiscale universal descriptors in describing the physics of GB. 
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