Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session U39: Machine learning for quantum matter VFocus Prize/Award
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Sponsoring Units: DCOMP GDS DMP Chair: Isaac Tamblyn, Natl Res Council Room: 703 |
Thursday, March 5, 2020 2:30PM - 3:06PM |
U39.00001: Nicholas Metropolis Award Talk: Enhancing Quantum Simulators with Neural Networks Invited Speaker: Giacomo Torlai Machine learning offers a set of flexible and powerful algorithms to enhance the capabilities of quantum simulation platforms. Artificial neural networks trained on measurement data can be integrated in the experimental stack for a variety of tasks, such as error mitigation, detecting quantum phase transitions and improving the measurement precision. I will review a data-driven framework for reconstructing quantum states prepared by experimental quantum hardware. Once trained, the neural networks can be used to deliver precise measurements of specialized observables that are either costly or not accessible in the original experimental setup. I will present results for a cold Rydberg-atom quantum simulator and quantum chemistry calculations on a superconducting quantum hardware. |
Thursday, March 5, 2020 3:06PM - 3:18PM |
U39.00002: Topological codes revisited: Hamiltonian learning and topological phase transitions Eliska Greplova, Agnes Valenti, Evert Van Nieuwenburg, Gregor Boschung, Frank Schäfer, Niels Loerch, Sebastian Huber The efficient validation of quantum devices is critical for emerging technological applications. The precise engineering of a Hamiltonian is required both for the implementation of quantum information processing as well as for quantum memories. Inferring the experimentally realized Hamiltonian through a scalable number of measurements constitutes the challenging task of Hamiltonian learning. In particular, assessing the quality of the implementation of topological codes is essential for quantum error correction. We introduce a neural net based approach to this challenge. We capitalize on a family of exactly solvable models to train our algorithm and generalize to a broad class of experimentally relevant sources of errors. We discuss how our algorithm scales with system size and analyze its resilience towards noise. A related issue regarding topological codes is to ensure that the system does not leave the topological manifold due to experimental noise. We present an unsupervised machine learning technique that is able to detect topological order from experimentally accessible data. |
Thursday, March 5, 2020 3:18PM - 3:30PM |
U39.00003: Real time evolution with neural network quantum states Irene Lopez Gutierrez, Christian Mendl The Hilbert space of a quantum system grows exponentially with system size, which makes many-body quantum systems challenging to simulate on a classical computer. One approach is to use tensor network methods, but these require an increasing bond dimension to capture the growth in entanglement during real time evolution, which limits their application to short time intervals. An alternative method proposed recently uses a neural network as a variational Ansatz to describe the quantum wave function. However, its application for real time evolution has not been extensively explored. In this work, we propose the use of standard machine learning optimization techniques, combined with a modified backpropagation for a neural network with complex parameters, to tackle the time evolution of an example system: the Ising model in 1 and 2-D. Our preliminary results show that our method performs comparably as well as stochastic reconfiguration, while avoiding a sensitivity issue related to the pseudo-inverse of the covariance matrix. |
Thursday, March 5, 2020 3:30PM - 3:42PM |
U39.00004: Hunting for Hamiltonians with a General-Purpose Symmetry-to-Hamiltonian Approach Eli Chertkov, Benjamin Villalonga, Bryan Clark Inverse methods that learn models from data are widely used in the field of machine learning to solve difficult engineering tasks. Recently, inverse methods have been applied in the context of quantum physics to engineer quantum models, i.e., Hamiltonians, with targeted properties, such as targeted eigenstates or reduced density matrices. Here we present a new efficient and general-purpose inverse method approach, the symmetric Hamiltonian construction (SHC), for engineering Hamiltonians with particular symmetries, such as integrals of motion or discrete symmetries [1]. This method extends on ideas developed in the slow operator method [2]. Using the SHC inverse method, we design new Hamiltonians with topological properties: superconducting Hamiltonians with Majorana zero modes and Z2 quantum spin liquid Hamiltonians. In this talk, we will introduce the SHC method and discuss the topological Hamiltonians that we find. Our open-source numerical implementation of the SHC method is available at github.com/ClarkResearchGroup/qosy. |
Thursday, March 5, 2020 3:42PM - 3:54PM |
U39.00005: Studying inhomogeneous quantum many-body problems using neural networks Alexander Blania, Evert Van Nieuwenburg, Florian Marquardt We show how convolutional neural networks can be employed to learn the mapping from arbitrary potential landscapes to observables in quantum many-body systems. While following the general spirit of density-functional theory, our approach can easily be applied without modification to a wide variety of settings, effectively learning the significant underlying physical principles from raw training data. We verify the performance of this framework for a number of examples such as the prediction of Friedel oscillations and level spacing statistics. Our network architecture allows us to predict on system sizes larger than seen in the training data, and we analyze its scaling performance |
Thursday, March 5, 2020 3:54PM - 4:06PM |
U39.00006: Calculating Wannier functions via basis pursuit using a machine learned dictionary Bradley Magnetta, Vidvuds Ozolins One of the earliest methods for calculating Wanner functions enforced localization by maximizing their projection onto a carefully chosen set of localized functions. Eventually use of this method faded with the emergence of more systematic approaches such as maximal localization. In this work we provide a modern method for calculating Wannier functions via projection by incorporating basis pursuit into the quantum variational method to automatically generate a set of localized functions needed to enforce localization while obtaining the ground state. We determine the dictionary to use for basis pursuit by performing sparse coding on a set of known Wannier functions. The algorithmic simplicity of our method suggests that it may be suited for automated calculation of Wannier functions. Other applications in physics that involve the variational principle could benefit from the inclusion of basis pursuit and sparse coding. |
Thursday, March 5, 2020 4:06PM - 4:18PM |
U39.00007: Classical Quantum Optimization with Neural Network Quantum States Joseph Gomes The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that had previously been intractable for existing exact numerical methods. Here, we demonstrate the utility of the variational representation of quantum states based on artificial neural networks for performing quantum optimization. We show empirically that this methodology achieves high approximation ratio solutions with polynomial classical computing resources for a range of instances of the Maximum Cut (MaxCut) problem whose solutions have been encoded into the ground state of quantum many-body systems up to and including 256 qubits. |
Thursday, March 5, 2020 4:18PM - 4:30PM |
U39.00008: Solving frustrated quantum many-particle models with convolutional neural networks Xiao Liang Recently, there has been significant progress in solving quantum many-particle problems via machine learning |
Thursday, March 5, 2020 4:30PM - 4:42PM |
U39.00009: Quantum dynamics in driven spin systems with neural-network quantum states Damian Hofmann, Giuseppe Carleo, Angel Rubio, Michael Sentef Neural-network quantum states (NQS) provide an effective variational representation of quantum states, which can be used for the study of many-body quantum systems [1]. NQS can be time-propagated using time-dependent variational Monte Carlo (tVMC) [1,2], making it possible to simulate non-equilibrium phenomena. In particular, this approach can be used to compute dynamical properties of two-dimensional spin systems [3], a setting that has proven to be challenging for established numerical techniques. In this talk, we study magnetic excitations in a driven two-dimensional Heisenberg antiferromagnet. Further, we provide benchmarks of time-dependent NQS against results obtained from exact calculations for small systems as well as results obtained using a time-dependent matrix product state (t-MPS) approach. |
Thursday, March 5, 2020 4:42PM - 4:54PM |
U39.00010: Study of phi-4 theories with deep learning methods Zhong Yuan Lai, Francisco Costa Meirinhos, Xiaopeng Li Field theories find wide applications from characterization of scattering processes in particle physics, to analysis of statistical models, to description of critical phenomena in condensed matter. One key problem in using field theories is to perform non-perturbative calculations, which is crucial in various places, but has remained an open question. In this talk I will present our recent work combining field theoretical and deep learning methods to systematically account for non-perturbative aspects. In calculating Green’s functions, nonperturbative Feynmann diagrams are automatically taken into account in our approach. I will present applications of this new approach to phi-4 field theories in one and two dimensions. Our approach potentially offers a generic solver for nonperturbative field theory calculations, of relevance to a broad context. |
Thursday, March 5, 2020 4:54PM - 5:06PM |
U39.00011: Unsupervised machine learning for accelerating discoveries from temperature dependent X-ray data Jordan Venderley, Michael Matty, Varsha Kishore, Geoff Pleiss, Kilian Weinberger, Eun-Ah Kim Data analysis is becoming an increasingly prominent bottleneck for many experimental fronts of quantum matter research. In particular, advancements in detector capabilities for X-ray and neutron scattering have enabled researchers to rapidly collect hundreds of GB of data. Here, we present a novel unsupervised machine learning approach for accelerating the analysis of temperature dependent single crystal X-ray diffraction data. Our method employs a mixture model to cluster over the temperature dependence of scattering intensities and readily identify phase transitions. It is capable of analyzing hundreds of GBs of data in the span of minutes, offering the tantalizing possibility of real time analysis. Applications to several materials are discussed. |
Thursday, March 5, 2020 5:06PM - 5:18PM |
U39.00012: Machine learning effective models for quantum systems Andrew Mitchell, Jonas Rigo The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. Using information theoretic techniques, we propose a model machine learning approach that optimizes an effective model based on an estimation of its partition function. The success of the method is exemplified by application to the single impurity Anderson model and double quantum dots, with new non-perturbative results obtained for the old problem of mapping to effective Kondo models. We also show that the correct effective model is not in general obtained by attempting to match observables to those of its parent Hamiltonian, due to information monotonicity along RG flow. |
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