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

T. H. Johnson, T. J. Elliott, S. R. Clark, D. Jaksch

Research output: Contribution to journalArticlepeer-review

8 Citations (SciVal)

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.
Original language English 090602 7 Physical Review Letters 114 9 5 Mar 2015 https://doi.org/10.1103/PhysRevLett.114.090602 Published - 6 Mar 2015

Keywords

• cond-mat.stat-mech
• quant-ph

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