A Score-Based Model for Learning Neural Wavefunctions

• URL: http://arxiv.org/abs/2305.16540v1
• Date: Thu, 25 May 2023 23:44:27 GMT
• Title: A Score-Based Model for Learning Neural Wavefunctions
• Authors: Xuan Zhang, Shenglong Xu, Shuiwang Ji
• Abstract summary: We provide a new framework for obtaining properties of quantum many-body ground states using score-based neural networks. Our new framework does not require explicit probability distribution and performs the sampling via Langevin dynamics.
• Score: 41.82403146569561
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum Monte Carlo coupled with neural network wavefunctions has shown success in computing ground states of quantum many-body systems. Existing optimization approaches compute the energy by sampling local energy from an explicit probability distribution given by the wavefunction. In this work, we provide a new optimization framework for obtaining properties of quantum many-body ground states using score-based neural networks. Our new framework does not require explicit probability distribution and performs the sampling via Langevin dynamics. Our method is based on the key observation that the local energy is directly related to scores, defined as the gradient of the logarithmic wavefunction. Inspired by the score matching and diffusion Monte Carlo methods, we derive a weighted score matching objective to guide our score-based models to converge correctly to ground states. We first evaluate our approach with experiments on quantum harmonic traps, and results show that it can accurately learn ground states of atomic systems. By implicitly modeling high-dimensional data distributions, our work paves the way toward a more efficient representation of quantum systems.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Quantum states from normalizing flows [0.0]
  We introduce an architecture for neural quantum states for many-body quantum-mechanical systems, based on normalizing flows. We demonstrate the use of this architecture for both ground-state preparation and real-time evolution.
  arXiv  Detail & Related papers  (2024-06-04T16:16:58Z)
• Towards a Foundation Model for Neural Network Wavefunctions [5.145741425164946]
  We propose a novel neural network ansatz, which maps uncorrelated, computationally cheap Hartree-Fock orbitals to correlated, high-accuracy neural network orbitals. This ansatz is inherently capable of learning a single wavefunction across multiple compounds and geometries.
  arXiv  Detail & Related papers  (2023-03-17T16:03:10Z)
• Wave function realization of a thermal collision model [0.0]
  An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling wave functions converging to a density operator description.
  arXiv  Detail & Related papers  (2022-09-20T07:24:40Z)
• Scalable neural quantum states architecture for quantum chemistry [5.603379389073144]
  Variational optimization of neural-network representations of quantum states has been successfully applied to solve interacting fermionic problems. We introduce scalable parallelization strategies to improve neural-network-based variational quantum Monte Carlo calculations for ab-initio quantum chemistry applications.
  arXiv  Detail & Related papers  (2022-08-11T04:40:02Z)
• Learnability of the output distributions of local quantum circuits [53.17490581210575]
  We investigate, within two different oracle models, the learnability of quantum circuit Born machines. We first show a negative result, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable. We show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable.
  arXiv  Detail & Related papers  (2021-10-11T18:00:20Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation [5.668795025564699]
  We present an approach for tackling open quantum system dynamics. We compactly represent quantum states with autoregressive transformer neural networks. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-09-11T18:00:00Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.