随机量子系统的多项式混沌展开模拟
Simulation of stochastic quantum systems using polynomial chaos expansions
摘要：
我们提出了一种基于多项式混沌展开的经典随机过程驱动的量子系统的模拟方法，多项式混沌展开是不确定性量化领域的一种著名技术。多项式混沌展开将系统密度矩阵表示为随机过程的主分量中的一系列正交多项式，并产生稀疏耦合的线性微分方程族。我们提供了实用的算法截断这种扩展的基础上，从时间依赖性微扰理论的结果，并证明，通过实验相关的一个量子位的数值例子，我们的技术可以显着更高的计算效率比蒙特卡罗模拟。
英文摘要：
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos expansion represents the system density matrix as a series of orthogonal polynomials in the principle components of the stochastic process and yields a sparsely coupled hierarchy of linear differential equations. We provide practical heuristics for truncating this expansion based on results from time-dependent perturbation theory and demonstrate, via an experimentally relevant one-qubit numerical example, that our technique can be significantly more computationally efficient than Monte Carlo simulation.
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