论文标题
用于嘈杂的广义特征值问题的修剪采样算法
Trimmed Sampling Algorithm for the Noisy Generalized Eigenvalue Problem
论文作者
论文摘要
解决广义特征值问题是找到大量子系统的能量特征态的有用方法。它使用对一组基础状态的投影通常不是正交的。一个人需要扭转一个矩阵，其条目是基础状态的内部产物，不幸的是，该过程也容易受到小错误的影响。当使用随机方法评估矩阵元素并具有明显的误差线时，问题尤其不错。在这项工作中，我们介绍了修剪的采样算法，以解决此问题。使用贝叶斯推论的框架，我们采样了由各种矩阵元素的不确定性估计和由物理信息约束组成的可能性函数确定的先验概率分布。结果是特征向量和可观察到的概率分布，该分布自动带有可靠的误差估计，并且执行远比标准正则化方法要好得多。该方法应立即用于涉及大量子系统的经典和量子计算计算的广泛应用。
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose entries are inner products of the basis states, and the process is unfortunately susceptible to even small errors. The problem is especially bad when matrix elements are evaluated using stochastic methods and have significant error bars. In this work, we introduce the trimmed sampling algorithm in order to solve this problem. Using the framework of Bayesian inference, we sample prior probability distributions determined by uncertainty estimates of the various matrix elements and likelihood functions composed of physics-informed constraints. The result is a probability distribution for the eigenvectors and observables which automatically comes with a reliable estimate of the error and performs far better than standard regularization methods. The method should have immediate use for a wide range of applications involving classical and quantum computing calculations of large quantum systems.
