论文标题
$ TimeEvolver $：时间演变的程序，有改进的错误绑定
$TimeEvolver$: A Program for Time Evolution With Improved Error Bound
论文作者
论文摘要
我们提出$ TimeEvolver $，这是一个用于计算通用量子系统中时间演变的程序。它依靠著名的Krylov子空间技术来解决将大型稀疏矩阵$ i H $的指数倍增的问题，其中$ h $是汉密尔顿人，最初的向量$ v $。 $ h $是Hermitian使得可以在Krylov近似的准确性方面易于计算的事实。除了数字圆形的影响外，与现有软件包相比，$ expokit $（R. Sidje，ACMTrans。Math。Soft。24（1）1998）与现有的软件包相比，后验误差绑定是严格的，这代表了至关重要的新颖性。在标准笔记本电脑上，$ TimeEvolver $允许在尺寸大于$ 10^6 $的希尔伯特空间中以可调节精度进行计算时间演变。此外，我们还提供了从哈密顿运营商的更抽象表示中得出矩阵$ h $的例程。
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.
