Hamiltonian simulation, i.e. simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful approximation can lead to relatively deep circuits. Here we start from the insight that for translation invariant systems, the gates in such circuit topologies can be further optimized on classical computers to decrease the circuit depth and/or increase the accuracy. We employ tensor network techniques and devise a method based on the Riemannian trust-region algorithm on the unitary matrix manifold for this purpose. For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements compared to fourth-order splitting methods. The optimized circuits could also be of practical use for the time-evolving block decimation algorithm.

中文翻译：

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用于哈密顿模拟的黎曼量子电路优化

哈密​​顿模拟，即模拟目标量子系统的实时演化，是量子计算的自然应用。 Trotter-Suzuki分裂方法可以生成相应的量子电路；然而，忠实的近似可能会导致相对较深的电路。在这里，我们从这样的见解开始：对于平移不变系统，这种电路拓扑中的门可以在经典计算机上进一步优化，以减少电路深度和/或提高准确性。为此，我们采用张量网络技术并设计了一种基于酉矩阵流形上的黎曼信赖域算法的方法。对于一维晶格上的伊辛和海森堡模型，与四阶分裂方法相比，我们实现了几个数量级的精度提高。优化的电路还可用于时间演化块抽取算法。