title: Capturing exponential variance using polynomial resources: applying tensor networks to nonequilibrium stochastic processes.
abstract: Estimating the expected value of an observable appearing in a nonequilibrium 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 e^{-βW}, motivated by Jarzynski's equality, with W the work done quenching from equilibrium at inverse temperature β, is exactly and efficiently captured by tensor networks.
authors: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore.|Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.|Keble College, University of Oxford, Parks Road, Oxford OX1 3PG, United Kingdom.|Institute for Scientific Interchange, Via Alassio 11/c, 10126 Torino, Italy.
authors: T H
authors: TH
authors: Johnson
authors: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
authors: T J
authors: TJ
authors: Elliott
authors: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore.|Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.|Keble College, University of Oxford, Parks Road, Oxford OX1 3PG, United Kingdom.
authors: S R
authors: SR
authors: Clark
authors: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore.|Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.|Keble College, University of Oxford, Parks Road, Oxford OX1 3PG, United Kingdom.
authors: D
authors: D
authors: Jaksch