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 $i H$, 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 $Expokit$ (R. Sidje, ACM Trans. Math. Softw. 24 (1) 1998). On a standard notebook, $TimeEvolver$ allows to compute time evolution with adjustable precision in Hilbert spaces of dimension greater than $10^6$. Additionally, we provide routines for deriving the matrix $H$ from a more abstract representation of the Hamiltonian operator.
翻译：我们提出了一个用于在通用量子系统中计算时间演变的程序,即“TimeEvolver$ ” 。它依靠众所周知的Krylov子空间技术来解决将大型稀薄矩阵指数乘以美元(H$是汉密尔顿人)的问题,即美元是汉密尔顿人,最初的矢量为美元。H美元是Hermitian人,使得能够根据Krylov近似值的准确性提供容易计算的费用。除了数字回合的影响外,由此产生的事后错误是严格的,与诸如“Expokit$”(R. Sidje,ACM Trans. Math. Softw. 24(1))等现有软件包相比,这是一个至关重要的新颖之处。在标准笔记本上,$TimeEvover$允许在Hilbert空间的可调整精确度超过10美元时进行计算。此外,我们提供了从汉密尔顿操作者更抽象的表述中得出美元矩阵值的例行做法。
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