Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes

Abstract

Estimating the expected value of an observable appearing in a non-equilibrium stochastic process usually involves sampling. If the observable's variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high variance observable ${\mathrm{e}}^{-\beta W}$, motivated by Jarzynski's equality, with $W$ the work done quenching from equilibrium at inverse temperature $\beta$, is exactly and efficiently captured by tensor networks.

7 pages, 3 figures, including supplemental material

References in corpus (31)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Tensor renormalization group approach to 2D classical lattice models
• Classical simulation of quantum many-body systems with a tree tensor network
• The iTEBD algorithm beyond unitary evolution
• Simulating quantum computation by contracting tensor networks
• Corner Transfer Matrix Renormalization Group Method
• Renormalization and tensor product states in spin chains and lattices
• Density Matrix Renormalization Group Method for 2D Classical Models
• Second Renormalization of Tensor-Network States
• Algorithms for finite Projected Entangled Pair States
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Renormalization of tensor-network states
• Ground State and Finite Temperature Lanczos Methods
• Density Matrix Renormalization Group and Reaction-Diffusion Processes
• Numerical Renormalization Group at Criticality
• Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0
• Go with the Winners: a General Monte Carlo Strategy
• Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem
• Dynamical simulations of classical stochastic systems using matrix product states
• Matrix Product States Algorithms and Continuous Systems
• Algebraically contractible topological tensor network states
• Stochastic Matrix Product States
• Reweighting for Nonequilibrium Markov Processes Using Sequential Importance Sampling Methods
• Computing probabilities of very rare events for Langevin processes: a new method based on importance sampling
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• Application of importance sampling to the computation of large deviations in non-equilibrium processes

Cited by in corpus (12)

• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Matrix Product Operators for Sequence to Sequence Learning
• Matrix Product States for Quantum Stochastic Modelling
• Efficient characterisation of large deviations using population dynamics
• Using tensor network states for multi-particle Brownian ratchets
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Measures of distinguishability between stochastic processes
• Entropy Governed by the Absorbing State of Directed Percolation
• Tensor-network algorithm for nonequilibrium relaxation in the thermodynamic limit
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation