Capturing exponential variance using polynomial resources: applying tensor networks to nonequilibrium stochastic processes.

Physical Review Letters
T H JohnsonD Jaksch

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.

References

Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E CarlonU Schollwöck
Aug 25, 2004·Physical Review Letters·Guifré Vidal
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hwee Kuan Lee, Yutaka Okabe
Oct 13, 2007·Physical Review Letters·Michael Levin, Cody P Nave
Nov 13, 2009·Physical Review Letters·Z Y XieT Xiang
Sep 28, 2010·Physical Review Letters·Kristan Temme, Frank Verstraete
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T H JohnsonD Jaksch
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Anupam KunduAbhishek Dhar

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Citations

Sep 17, 2019·Physical Review Letters·Kenji Harada, Naoki Kawashima
Jan 13, 2019·Physical Review Letters·Chengran YangMile Gu
Jul 22, 2020·Physical Review. E·Chengran YangThomas J Elliott
Aug 22, 2018·Nature Communications·A StrathearnB W Lovett

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