Large-scale full-programmable quantum walk and its applications

分类： 光学 >> 量子光学 提交时间： 2023-02-19

Yizhi Wang Yingwen Liu Junwei Zhan Shichuan Xue Yuzhen Zheng Ru Zeng Zhihao Wu Zihao Wang Qilin Zheng Dongyang Wang Weixu Shi Xiang Fu Ping Xu Yang Wang Yong Liu Jiangfang Ding Guangyao Huang Chunlin Yu Anqi Huang Xiaogang Qiang

摘要： With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum walks are powerful kernels for developing new and useful quantum algorithms. Here we realize large-scale quantum walks using a fully programmable photonic quantum computing system. The system integrates a silicon quantum photonic chip, enabling the simulation of quantum walk dynamics on graphs with up to 400 vertices and possessing full programmability over quantum walk parameters, including the particle property, initial state, graph structure, and evolution time. In the 400-dimensional Hilbert space, the average fidelity of random entangled quantum states after the whole on-chip circuit evolution reaches as high as 94.29$\pm$1.28$\%$. With the system, we demonstrated exponentially faster hitting and quadratically faster mixing performance of quantum walks over classical random walks, achieving more than two orders of magnitude of enhancement in the experimental hitting efficiency and almost half of the reduction in the experimental evolution time for mixing. We utilize the system to implement a series of quantum applications, including measuring the centrality of scale-free networks, searching targets on Erd\"{o}s-R\'{e}nyi networks, distinguishing non-isomorphic graph pairs, and simulating the topological phase of higher-order topological insulators. Our work shows one feasible path for quantum photonics to address applications of practical interests in the near future.

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