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量子模拟是利用可控的量子系统来模拟其他未知或难以控制的量子体系, 通过这种方法来处理一些在经典计算机上无法进行仿真的复杂量子体系, 用于如基础物理探索、分子动力学研究、药物研发等相关领域. 集成光学系统是实现量子模拟的一个优秀的实验平台, 能实现如无序系统、拓扑绝缘体、非线性和非厄米体系等凝聚态物理结构的模拟, 或用于实现量子随机行走、玻色取样等以演示量子优越性. 本文介绍多种量子模拟物理模型的理论基础, 结合如硅、玻璃、铌酸锂等波导体系的优势, 综述近年来利用集成光芯片实现量子模拟的研究进展, 包括了在集成光芯片上基于模拟型和数字型这两类量子模拟实现凝聚态物理模型仿真、量子随机行走、玻色取样等, 探讨集成光芯片上的不同的量子模拟技术的实用化前景和发展趋势.Quantum simulation is to use a controllable quantum system to simulate other complicated or hard-to-control quantum system, and to deal with some complex unknown quantum systems that cannot be simulated on classical computers due to the exponential explosion of the Hilbert space. Among different kinds of physical realizations of quantum simulation, integrated optical systems have emerged as an appropriate platform in recent years due to the advantages of flexible control, weak decoherence, and no interaction in optical systems. In this review, we attempt to introduce some of the basic models used for quantum simulation in integrated photonic systems. This review article is organized as follows. In Section 2, we introduce the commonly used material platforms for integrated quantum simulation, including the silicon-based, lithium niobate-based integrated circuits, and the femtosecond laser direct writing optical waveguides. Several integrated optical platforms such as the coupled waveguide arrays, photonic crystals, coupled resonator arrays, and multiport interferometers are also introduced. In Section 3, we focus on the analog quantum simulations in the integrated photonic platform, including Anderson localization of light in disordered systems, various kinds of topological insulators, nonlinear and non-Hermitian systems. More specifically, in Subsection 3.1, we present the integrated photonic realizations of disordered and quasi-periodic systems. In Subsection 3.2, we review the integrated photonic realizations of the topological insulators with and without time-reversal symmetry, including Floquet topological insulators, quantum spin hall system, anomalous quantum hall system, valley hall system, Su-Schrieffer-Heeger (SSH) model, and photonic topological Anderson insulators. Besides, topological insulator lasers and topologically protected quantum photon sources are briefly reviewed. In Subsection 3.3, we review the nonlinear and non-Hermitian integrated optical systems. In Section 4 we present the integrated digital quantum simulations based on the multiport interferometers, including the discrete-time quantum random walk, Boson sampling, and molecular simulation. In Section 5, we summarize the content of the article and present the outlook on the future perspectives of the integrated photonic quantum simulation. We believe that the integrated photonic platforms will continue to provide an excellent platform for quantum simulation. More practical applications will be found based on this system through combining the fields of topological photonics, laser technologies, quantum information, nonlinear and non-Hermitian physics.
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Keywords:
- quantum simulation /
- integrated photonic circuits /
- simulation of condensed matter physics /
- multiport interferometer
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图 2 用于模拟拓扑绝缘体结构的耦合环腔阵列 (a) 量子自旋霍尔效应系统[59]; (b) 周期驱动Floquet拓扑绝缘体结构[60]; (c) 反常量子霍尔效应系统[63]. (a)—(c)上列为周期阵列结构, 下列为周期结构中基本单元的物理图像
Fig. 2. Arrays of coupled ring resonators for simulations of topological insulators: (a) Quantum spin Hall effect[59]; (b) Floquet topological insulators[60]; (c) anomalous quantum Hall effect[63]. The upper panel in (a)–(c): periodic coupled resonator arrays; lower panel: basic units in the periodic structures.
图 3 多端口干涉仪用于量子模拟 (a) 三角形结构(左)[66]和矩形结构(右)[67]的多端口干涉仪用于实现任意的幺正变换; (b)双光子在离散型量子随机行走芯片中的安德森局域化现象[14]; (c) 硅基多端口干涉仪[68], 由可调马赫-曾德尔干涉仪组成
Fig. 3. Multiport interferometer for quantum simulation: (a) Realizing arbitrary unitary operator using triangular (left)[66] and rectangular (right)[67] mesh of beam splitters; (b) two-photon Anderson localization in discrete-time quantum random walk circuits[14]; (c) multiport interferometer in a silicon-on-insulator platform[68], which is consist of tunable Mach-Zehnder interferometers.
图 4 (a) 二维无序光子晶格中的安德森局域化现象[76]; (b) 一维准周期飞秒激光直写光波导阵列[85]; (c) 飞秒激光直写螺旋式波导阵列结构实现Floquet拓扑绝缘体[25]; (d) 弯曲波导阵列实现等效磁场, 模拟Aharonov-Bohm效应[89]; 在耦合环腔阵列结构中产生(e) 拓扑绝缘体激光[90]、(f) 拓扑保护多光子量子光源[91]; (g) 基于谷光子晶体结构设计等比分束器并实现双光子量子干涉[57]; (h) 无序拓扑安德森绝缘体结构[92]; (i) 基于一维SSH模型在硅基结构中产生关联光子对[93]; (j) “含时”哈密顿量系统用于研究拓扑泵浦[87]; (k) 奇偶-时间对称与对称破缺交界面处局域的拓扑边界态[94]; (l) 非厄米SSH模型中非线性对奇偶-时间对称相变过程的影响[22]
Fig. 4. (a) Anderson localization in a two-dimensional photonic lattice[76]; (b) simulation of one-dimensional quasicrystals in femtosecond-laser-written (FLW) optical waveguides[85]; (c) realization of photonic Floquet topological insulators in a FLW helical waveguide array[25]; (d) realization of an effective magnetic field and simulation of Aharonov-Bohm effect using curved waveguide arrays[89]; generation of (e) topological insulator laser[90] and (f) multiphoton quantum source[91] in coupled resonator arrays; (g) design of a 1∶1 topological beam splitter in valley photonic crystals and realize the two-photon quantum interference[57]; (h) photonic topological Anderson insulator[92]; (i) generation of biphoton state in a SSH photonic lattice[93]; (j) topological pumping in a system described by a time-varying Hamiltonian[87]; (k) topological edge state in a photonic lattice at the interface between the structures with and without parity-time symmetry[94]; (l) nonlinear tuning of PT symmetry and non-Hermitian topological states[22].
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