Neural Projected Quantum Dynamics: a systematic study

Abstract

We investigate the challenge of classical simulation of unitary quantum dynamics with variational Monte Carlo approaches, addressing the instabilities and high computational demands of existing methods. By systematically analyzing the convergence of stochastic infidelity optimizations, examining the variance properties of key stochastic estimators, and evaluating the error scaling of multiple dynamical discretization schemes, we provide a thorough formalization and significant improvements to the projected time-dependent Variational Monte Carlo (p-tVMC) method. We benchmark our approach on a two-dimensional Ising quench, achieving state-of-the-art performance. This work establishes p-tVMC as a powerful framework for simulating the dynamics of large-scale two-dimensional quantum systems, surpassing alternative VMC strategies on the investigated benchmark problems.

32 pages, 13 figures, 7 tables

References in corpus (62)

• Quantum Computing in the NISQ era and beyond
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Quantum Simulation
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Neural Tangent Kernel: Convergence and Generalization in Neural Networks
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Time-evolution methods for matrix-product states
• Tensor networks for complex quantum systems
• Quantum Natural Gradient
• Theory of variational quantum simulation
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Quantum Entanglement in Neural Network States
• Tensor network states and geometry
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Fermionic neural-network states for ab-initio electronic structure
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Finding Exponential Product Formulas of Higher Orders
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Variational neural network ansatz for steady states in open quantum systems
• A positive tensor network approach for simulating open quantum many-body systems
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Latent Space Purification via Neural Density Operators
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Tensor Network Algorithms: a Route Map
• Unifying Projected Entangled Pair States contractions
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Solving frustrated quantum many-particle models with convolutional neural networks
• Neural tensor contractions and the expressive power of deep neural quantum states
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Transformer variational wave functions for frustrated quantum spin systems
• Neural network wave functions and the sign problem
• Quenches near Ising quantum criticality as a challenge for artificial neural networks
• Discovering Quantum Phase Transitions with Fermionic Neural Networks
• Classical variational simulation of the Quantum Approximate Optimization Algorithm
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Empowering deep neural quantum states through efficient optimization
• Variational Benchmarks for Quantum Many-Body Problems
• One-dimensional many-body entangled open quantum systems with tensor network methods
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension
• Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution
• Neural-network quantum states for many-body physics
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics
• Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Unitary dynamics of strongly-interacting Bose gases with time-dependent variational Monte Carlo in continuous space
• Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation
• Entanglement detection with classical deep neural networks
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Real-time Dynamics of the Schwinger Model as an Open Quantum System with Neural Density Operators
• Scalable Imaginary Time Evolution with Neural Network Quantum States
• Empirical Sample Complexity of Neural Network Mixed State Reconstruction
• Amplitude Ratios and Neural Network Quantum States
• Efficiency of neural quantum states in light of the quantum geometric tensor

Cited by in corpus (7)

• Predicting Topological Entanglement Entropy in a Rydberg analog simulator
• Non-stabilizerness of Neural Quantum States
• Time-dependent Neural Galerkin Method for Quantum Dynamics
• Design principles of deep translationally-symmetric neural quantum states for frustrated magnets
• Generalized Lanczos method for systematic optimization of neural-network quantum states
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model