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

### Reference:

Johnson, T. H., Elliott, T. J., Clark, S. R. and Jaksch, D., 2015. Capturing exponential variance using polynomial resources:applying tensor networks to non-equilibrium stochastic processes. Physical Review Letters, 114 (9), 090602.

### Related documents:

 Other (Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes) Download (454kB)

### Official URL:

http://dx.doi.org/10.1103/PhysRevLett.114.090602

### 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.

### Details

 Item Type Articles Creators Johnson, T. H., Elliott, T. J., Clark, S. R. and Jaksch, D. DOI 10.1103/PhysRevLett.114.090602 Uncontrolled Keywords cond-mat.stat-mech,quant-ph Departments Faculty of Science > Physics Refereed Yes Status Published ID Code 47354 Additional Information 7 pages, 3 figures, including supplemental material