论文标题
部分可观测时空混沌系统的无模型预测
Implementation of Continuous-Time Quantum Walks on Quantum Computers
论文作者
论文摘要
量子步行是模拟复杂量子系统并构建量子算法的有用模型；特别是，在图上开发空间搜索算法，旨在尽快找到标记的顶点。量子步行是在量子计算机上实施的有趣候选者。在这项工作中，我们描述了在三个图类类别上实现基于连续时间量子 - 步行的搜索算法的进化运算符的有效电路：完整的图，完整的两部分图和超启机。对于完整和完整的两部分图的类别，电路准确地实现了进化运算符。对于高管类别，电路实现了近似进化算子，当顶点数量较大时，该电路倾向于确切的进化算子。我们的Qiskit模拟表明，即使对于低维高管，该实现也成功地找到了标记的顶点。
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are interesting candidates to be implemented on quantum computers. In this work, we describe efficient circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms on three graph classes: complete graphs, complete bipartite graphs, and hypercubes. For the class of complete and complete bipartite graphs, the circuits implement the evolution operator exactly. For the class of hypercubes, the circuit implements an approximate evolution operator, which tends to the exact evolution operator when the number of vertices is large. Our Qiskit simulations show that the implementation is successful at finding the marked vertex even for low-dimensional hypercubes.
