Experimental Realization of Quantum Walks

Schematic diagram of photonics quantum walks experimental device.

Quantum walks, the counterpart of classical random walk, have essential differences between its classical one. There are many examples of classical random walks, such as Galton board and Brownian motion. In classical random walk, it is probability that superposed in the walk process, but it is amplitude in corresponding quantum walks. The probability distribution of walkers of these two kinds of walks is fundamentally different. In particular, the diffusion velocity of quantum walks is quadratic enhancement of spreading than classical random walks. In the contribution of these unique characters, quantum walks have been applied in quantum information process, quantum computation and other various areas.

However, the quantum states cannot be manipulated easily, the stability of experimental system and the coherence of quantum state cannot be kept for a long time. These difficulties make the experimental implementation of quantum walks very challenging. Therefore, a lot of physical systems have been explored to realize quantum walks to overcome the problem of controllability, such as trapped atoms, trapped ions and photonic systems. On the other hand, when photons walk in the structure of fiber or waveguide, the coherence of photons can also be preserved for walking a large number of steps. As these various realizations of quantum walks, the applications of quantum walks have been explored in many fields.

Quantum walks have been realized in a lot of physical systems. The applications of photonic quantum walks are particularly highlighted. Since photons have multiple degrees of freedom that can be controlled flexibly, photonic quantum walks offer excellent performance such as high degree of flexibility, expandability and integration when coding information with photons.

The team from Beijing computational science research center has been keeping the record of the longest steps of photonic quantum walks in free space, and has done a series of research work on quantum simulation, quantum measurement and verification of the basic principles of quantum mechanics. The team made a detailed summary of the implementation of photonic quantum walks on the basis of different degrees of freedom (such as polarization path and orbital angular momentum), as well as different experimental structures (such as linear optical crystals in a straight line, fiber loop and waveguide). Meanwhile the respective advantages and disadvantages were also compared. The results have been published in Chinese Optics Letters, Vol. 18, Issue 5, 2020 (Gaoyan Zhu, Lei Xiao, Bingzi Huo, Peng Xue. Photonic discrete-time quantum walks [Invited][J]. Chinese Optics Letters, 2020, 18(5): 052701).

Professor Xue, leader of the team, said that there contain great application potentials of quantum walks. In the aspect of quantum information procession, quantum walks can act as a universal tool box for implementation of arbitrary two-dimension or higher-dimensional systems, single or multiple unitary/non-unitary evolutions, and quantum information processing.

In terms of quantum computing, quantum walks can be applied to develop big data search algorithm, differential evolution algorithm and Boson sampling algorithm. The multi-body non-unitary quantum walks can be explored for measurements of topological properties, based on which, topological quantum computation can be realized.

In the future, experimental research on photonic quantum walks will be mainly carried out in optical fiber structures and waveguide structures. These structures are easy to integrate and are the basis for the development and application of quantum processors.

光量子行走的实验实现

光量子行走实验装置示意图

量子行走作为经典随机行走在量子世界的对应，和经典随机行走有着本质的不同。经典随机行走比较常见的例子有布朗运动、高尔顿板等，其行走过程是几率的叠加。而量子行走中因为量子态的叠加性，行走过程是几率幅的叠加。这一本质区别导致量子行走中行走者的位置分布与经典完全不同，并且分布的扩散速度呈现二次方式的增长。正是由于量子行走这些不同的特点，使得量子行走在量子信息和量子计算等诸多领域有着广泛的应用。

由于量子态的操控性不够灵活、实现量子行走的系统难以长时间稳定、量子态的相干性难以保持等因素的存在，使得在实验上研究量子行走具有诸多挑战。为克服这些困难，一方面，通过实验实现了诸如原子、离子、光子等系统的量子行走，以解决灵活操控的问题。另一方面，将波导结构、光纤结构等特殊的实验结构用以实现量子行走，可以很好地解决退相干的问题。多种多样的量子行走的实验实现，使得量子行走的研究被广泛应用于各个领域。

量子行走已在多种实验体系中得以实现，且以光子系统的应用最为突出。由于光子有着多个可以操控的自由度，使得单光子作为信息的良好载体，在量子行走中有着操控灵活、可扩展性强、便于集成等优势。

来自北京计算科学研究中心的科研团队一直保持着实验上实现了光量子行走在自由空间行走步数最长的记录，并在量子行走中关于量子模拟、量子测量和量子力学基本原理验证等问题做了一系列研究工作。相关综述发表在Chinese Optics Letters 2020年第5期（Gaoyan Zhu, Lei Xiao, Bingzi Huo, Peng Xue. Photonic discrete-time quantum walks [Invited][J]. Chinese Optics Letters, 2020, 18(5): 052701）。

在本篇综述中，他们着眼于光量子行走的实验实现，除了团队的一系列研究工作之外，还从实现行走的光子的偏振、路径、轨道角动量等不同的自由度和行走装置的不同结构，做了详细的分析和总结，讨论了各种不同系统实现量子行走的过程，以及它们各自的优缺点。

团队负责人薛鹏教授认为，量子行走具有极大的应用价值：在量子信息处理方面，量子行走 可以作为一种通用的工具箱，实现任意的两维或者高维体系、单体或者多体的幺正/非幺正演化，进而实现量子信息处理的所有关键步骤；在量子计算方面，量子行走除了可以开发一系列的量子算法之外，还被证明可以实现通用的量子计算。另外，通过设计并实现多体的非幺正量子行走模型，研究其独特的拓扑特性，未来有望实现拓扑量子计算。

未来，关于光量子行走的实验研究，将会偏向于在光纤结构和波导结构中实现，这些结构便于集成，是实现量子信息处理器芯片化和实用化的基础。