Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session D62: Machine Learning for Quantum Matter IFocus
|
Hide Abstracts |
Sponsoring Units: DCOMP Chair: Ziyan Zhu, Stanford University Room: Room 417 |
Monday, March 6, 2023 3:00PM - 3:36PM |
D62.00001: Recurrent neural networks for many-body physics Invited Speaker: Juan Carrasquilla I will discuss our recent work on the use of autoregressive neural networks for many-body physics. In particular, I will discuss two approaches to represent quantum states using these models and their applications to the reconstruction of quantum states, the simulation of real-time dynamics of open quantum systems, and the approximation of ground states of many-body systems displaying long-range order, frustration, and topological order. Finally, I will discuss how annealing in these systems can be used for combinatorial optimization where we observe solutions to problems that are orders of magnitude more accurate than simulated and simulated quantum annealing. |
Monday, March 6, 2023 3:36PM - 3:48PM |
D62.00002: Self-Averaging of Digital MemComputing Machines Daniel Primosch Digital MemComputing machines (DMMs) are a new class of computing machines that employ non-quantum dynamical systems with memory to solve combinatorial optimization problems [1]. We show that the time to solution (TTS) of DMMs follows an inverse Gaussian distribution, with the TTS self-averaging with increasing problem size, irrespective of the problem they solve. We provide both an analytical understanding of this phenomenon and numerical evidence by solving hard instances of the 3-SAT (satisfiability) problem. The self-averaging property of DMMs with problem size implies that they are increasingly insensitive to the detailed features of the instances they solve, by leveraging global information over local information as the problem size increases. This is in sharp contrast to traditional algorithms applied to the same problems, illustrating another advantage of this physics-based approach to computation. |
Monday, March 6, 2023 3:48PM - 4:00PM |
D62.00003: A deep learning approach to quantum many-body physics with space group symmetries Tianshu Huang Artificial neural networks (ANNs) have been utilized as an inexpensive wave function Ansatz together with quantum Monte Carlo (QMC) methods to solve quantum many-body systems. Such an approach has achieved success in solving 1D and 2D spin systems but also struggled with the exponential growth of complexity with respect to the size of the system. In order to overcome such an obstacle, the approach has to adopt network architectures and incorporate methods that perform effective dimensionality reduction and feature extraction. In this work, we demonstrate an ANN-QMC approach that uses a modified convolutional neural network architecture as the wave function Ansatz. We incorporate space group symmetry in the Monte Carlo sampling process to reduce system complexity. We test our approach on a fermionic model, the 2D Hubbard model on square lattices at half-filling, and approximate the ground state energy of the system. |
Monday, March 6, 2023 4:00PM - 4:12PM |
D62.00004: Solving quantum many-body problems by combining artificial neural network with variational Monte Carlo Xiaowei Ou Artificial neural networks have been successfully incorporated with variational Monte Carlo (VMC) to study quantum many-body problems. In this study, we propose a modified neural network architecture to represent ground-state wave functions, using separate convolutional channels of different widths and depths for the amplitude and phase of the wave function. A Hamiltonian matrix tree search and importance sampling VMC are used to improve the efficiency of the Markov chain sampling for gradient-based optimization of the ground-state energy. Space group symmetry of the lattice is also included to reduce the computational complexity and obtain quantum many-body states at a given k point. This framework is demonstrated by computing the ground-state energy of strong interacting quantum spin models. |
Monday, March 6, 2023 4:12PM - 4:24PM |
D62.00005: Towards Neural Variational Monte Carlo That Scales Linearly with System Size Or Sharir, Garnet K Chan, Anima Anandkumar Quantum many-body problems are some of the most challenging problems in science and are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, coupled with the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. However, the run-time of this approach scales quadratically with the number of simulated particles, constraining the practically usable NN to — in machine learning terms — minuscule sizes ( |
Monday, March 6, 2023 4:24PM - 4:36PM |
D62.00006: Systematic improvement of neural network quantum states using Lanczos Hongwei Chen, Douglas G Hendry, Phillip E Weinberg, Adrian E Feiguin The quantum many-body problem lies at the center of the most important open challenges in condensed matter, quantum chemistry, atomic, nuclear, and high-energy physics. While quantum Monte Carlo, when applicable, remains the most powerful numerical technique capable of treating dozens or hundreds of degrees of freedom with high accuracy, it is restricted to models that are not afflicted by the infamous sign problem. A powerful alternative that has emerged in recent years is the use of neural networks as variational estimators for quantum states. In this work, we propose a symmetry-projected variational solution in the form of linear combinations of simple restricted Boltzmann machines. This construction allows one to explore states outside of the original variational manifold and increase the representation power with moderate computational effort. Besides allowing one to restore spatial symmetries, an expansion in terms of Krylov states using a Lanczos recursion offers a solution that can further improve the quantum state accuracy. We illustrate these ideas with an application to the Heisenberg $J_1-J_2$ model on the square lattice, a paradigmatic problem under debate in condensed matter physics, and achieve state-of-the-art accuracy in the representation of the ground state. |
Monday, March 6, 2023 4:36PM - 4:48PM |
D62.00007: Progress on the simulation of ab-initio Hamiltonians using neural network quantum states Javier Robledo Moreno, jeffrey cohn, Mario Motta, Jannes Nys, Giuseppe Carleo, Antoine Georges The variational simulation of electronic systems requires the parametrization of the wave function amplitudes on a given single-particle basis. Working in first (second) quantization, the parametrized wave function amplitudes must be anti-symmetric (symmetric) functions of the particle configurations, while being able to capture correlations beyond single-particle Slater determinants. To date, multiple candidates have been proposed in the space of neural-network (NN) parametrizations. While much progress has been made in the design of NN-based parametrizations, there are still open questions regarding their accuracy to describe the ground-state properties of ab-initio Hamiltonians. |
Monday, March 6, 2023 4:48PM - 5:00PM |
D62.00008: Fermionic isometric tensor network states in 2D Zhehao Dai, Yantao Wu, Taige Wang, Michael P Zaletel In one dimension, the density-matrix renormalization group (DMRG) algorithm gives practically exact ground state wavefunctions and energies for gapped systems and good approximations of ground states for gapless systems. The success of 1D DMRG relies on the structure of tensor network states (TNS), an efficient representation of |
Monday, March 6, 2023 5:00PM - 5:12PM |
D62.00009: Constructing realistic tight-binding models via differentiable programming Mengli Hu Differentiable programming(DP) is a programming paradigm of evaluating derivatives by applying automatic differentiation, which can handle a large scale of parameters. With its high efficiency and accuracy, DP has been widely used in machine learning and other gradient-based optimization(GBO) problems. In this letter, we implement DP in constructing realistic tight-binding(TB) models that usually have a large number of parameters. By fitting the band structure from the first-principles calculation, building a realistic TB model can be transformed into a GBO problem. We first analyzed the computation graph and demonstrated that the time complexity of DP is O(N) which is much smaller than O(N2) in the conventional finite differentiation, where N is the number of parameters. Then, we further explicitly demonstrate the power of our new method to build the TB model for silicon with around 7*104 parameters, which cannot be accomplished with finite differentiation. Moreover, other physics constraints in building TB models, such as symmetry requirements, can be attached to the GBO process due to the great flexibility and compatibility of DP. Our work provides an efficient and accurate method to construct realistic TB models suitable for large-scale simulations of real materials. |
Monday, March 6, 2023 5:12PM - 5:24PM |
D62.00010: Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation Stephan Humeniuk, Yuan Wan, Lei Wang Direct sampling from a Slater determinant is combined with an autoregressive deep neural network |
Monday, March 6, 2023 5:24PM - 5:36PM |
D62.00011: Unreasonable effectiveness of pairwise Markov random fields in finding ground states of stoquastic Hamiltonians Yuchen Pang, Abhijith J., Evan McKinney, Carleton Coffrin, Marc Vuffray, Andrey Y Lokhov We introduce auto-regressive Markov random fields (MRF) as an ansatz for finding the ground states of stoquastic Hamiltonians. Using exact MRF learning methods, we find that an auto-regressive representation with only pairwise interactions can faithfully represent the ground states of many important classes of Hamiltonians, including frustrated and disordered models. For larger systems, we observe that this pairwise ansatz coupled with first-order optimization methods is capable of outperforming established methods in quantum-dominated regions of the phase space. Our work thus illustrates the computational benefits of the auto-regressive pairwise MRFs in capturing the ground-state properties of stoquastic quantum models. |
Monday, March 6, 2023 5:36PM - 5:48PM |
D62.00012: Spectral Gaps via Imaginary Time Jacob Leamer, Alicia B Magann, Denys I Bondar Many open problems in physics from the Haldane conjecture regarding Heisenberg models with integer spins to the existence of the topological spin liquid phase to the Yang-Mills mass gap problem, one of the famed millennium problems, and an explanation of quark confinement are concerned with spectral gaps. The spectral gap is the energy difference between the ground and first excited states of a system and governs many of its behaviors, especially at lower energy. We show that the spectral gap can be calculated as a simple ratio of the two expectation values calculated over the wave function propagated in imaginary time. This method constitutes a significant simplification over the existing methods for spectral gap calculation. We demonstrate the effectiveness of this method on the Fermi-Hubbard and transverse field Ising models. Additionally, we discuss the implementation of the method on a quantum computer. Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525. SAND2022-14593 A. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700