TY - JOUR

T1 - Capturing exponential variance using polynomial resources

T2 - Applying tensor networks to nonequilibrium stochastic processes

AU - Johnson, T. H.

AU - Elliott, T. J.

AU - Clark, S. R.

AU - Jaksch, D.

PY - 2015/3/5

Y1 - 2015/3/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84924359782&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.114.090602

DO - 10.1103/PhysRevLett.114.090602

M3 - Article (Academic Journal)

C2 - 25793792

AN - SCOPUS:84924359782

VL - 114

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 9

M1 - 090602

ER -