论文标题
部分可观测时空混沌系统的无模型预测
Riemannian quantum circuit optimization for Hamiltonian simulation
论文作者
论文摘要
哈密顿模拟，即模拟目标量子系统的实时演变，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；但是，忠实的近似可能会导致相对较深的电路。在这里，我们从以下见解开始：对于翻译不变系统，可以在经典计算机上进一步优化此类电路拓扑中的门，以减少电路深度和/或提高精度。我们采用张量化网络技术，并设计一种基于Riemannian Trust-Region算法的方法，用于此目的。对于一维晶格的Ising和Heisenberg模型，与四阶分裂方法相比，我们实现了数量级的精度。优化的电路也可以用于随时间不断发展的块拆卸（TEBD）算法。
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 (TEBD) algorithm.
