线性光学量子行走在量子模拟中的应用研究

Quantum simulation is an important research field in quantum information science, whose goal is to build up special purpose devices based on controllable quantum systems for investigating the property and dynamics of complex quantum systems, which is difficult to study in the laboratory and impossible to model with a supercomputer. Different from the universality of quantum computation, quantum simulators are usually customized for special problems and work under the rules of quantum mechanics. Quantum walks, as a simple and intuitive physical model, has various applicability, even for constructing universal quantum computation. This project will focus on investigating the applications of quantum walks to quantum simulation, constructing special quantum simulators based on the experimental system of time multiplexing linear optical quantum walks. Firstly, by realizing coin operation varying with the walk steps and reconstructing the final state in momentum space, directly observe the topological phase and investigate the topological structure in quantum walks. Secondly, by realizing a universal coin.operation changing both with the walk steps and walker’s position, realize the simulation of some complex quantum systems, such as the generation of Schodinger cat state, observing the Dirac zitterbewegung, etc. Moreover, try to implement experimental demonstrations of some quantum algorithms. The implementation of this project will provide new insights and novel applications on these critical problems, meanwhile put forward the research on quantum simulation and quantum computation.

量子模拟是量子信息领域的一个重要研究方向，其目标是利用一个特别设计的可控量子系统研究经典计算机难以解决的复杂量子系统的性质和演化。区别于量子计算机的通用性，量子模拟器一般是针对特定研究对象专门设计的按照量子力学规律运行的装置。量子行走作为一个简单直观的物理模型，其应用前景非常广阔，基于该模型甚至可以构建普适量子计算。本项目着重探索量子行走在量子模拟方向的应用，拟基于时间复用的线性光学量子行走实验系统实现特定的量子模拟器：实现随行走步数周期变化的硬币操作，通过测量动量空间系统末态，直接观察量子行走中的拓扑相，研究量子行走中的拓扑结构；通过调节硬币操作随行走者位置和行走步数的任意变化，实现较为复杂的系统的量子模拟，如制备薛定谔猫态、模拟Dirac颤动等；探索完成一些基于量子行走的量子算法的实验实现。本项目的实施将深化对这些重要问题的理解和应用，并推动量子模拟和量子计算的发展。

离散时间量子行走作为一个支持拓扑的天然的周期性驱动动力学系统，特别适合进行对无相互作用多体系统的量子模拟。在本项目的资助下，项目负责人领导课题组在前期工作的基础上，成功搭建其具有一定规模、支持单光子的光量子行走实验系统，开展了系列的量子模拟相关工作。通过建立与量子行走对应的多体模型，揭示了量子行走中动力学拓扑序参数的非解析变化与发生动力学量子相变之间的内在联系，提出并实验验证量子行走中纠缠鲁棒性在不同拓扑相下存在显著差异，并以此进一步实现了拓扑相及其相变的探测。