TimeEvolver: A program for time evolution with improved error bound

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where H is the Hamiltonian, with an initial vector v. The fact that H is Hermitian makes it possible to provide an easily computable bound on the accuracy of the Krylov approximation. Apart from effects of numerical roundoff, the resulting a posteriori error bound is rigorous, which represents a crucial novelty as compared to existing software packages such as Expokit [1]. On a standard notebook, TimeEvolver allows to compute time evolution with adjustable precision in Hilbert spaces of dimension greater than 106. Additionally, we provide routines for deriving the matrix H from a more abstract representation of the Hamiltonian operator.

本报告推出TimeEvolver程序，该程序用于计算通用量子系统中的时间演化。该程序依赖已知的Krylov子空间技术来解决大稀疏矩阵iH的指数乘法问题，其中H为哈密顿量，v为初始矢量。由于H为厄米矩阵，因此能够提供易于计算的Krylov逼近精度上界。除数值舍入误差外，所得的后验误差界是严格的，相较于现有的软件包如Expokit[1]，此为一大创新。在标准笔记本上，TimeEvolver允许在维度大于10^6的希尔伯特空间中，以可调节的精度计算时间演化。此外，我们还提供了从哈密顿算符的更抽象表示中导出矩阵H的例程。