Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes
Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes
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DOI：
10.1103/physrevlett.114.090602
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发表时间：
2015-03-05
影响因子：
8.6
通讯作者：
Jaksch, D.
中科院分区：
文献类型：
--
作者：
Johnson, T. H.;Elliott, T. J.;Jaksch, D.
估计出现在非平衡随机过程中的可观测值的期望值通常涉及抽样。如果观测值的方差很高，则需要许多样本。相比之下，我们表明，使用张量网络压缩在不采样的情况下执行相同的任务，可以有效地捕获各种几何形状和尺寸的系统中的高方差。我们提供的例子，匹配我们的有效方法的准确性将需要一个样本大小与系统大小呈指数级缩放。特别是，由Jarzynski等式激发的高方差可观测e（-beta W），其中W是在逆温度β下从平衡淬火完成的功，被张量网络准确有效地捕获。
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(-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.