Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs

Tong Wu (吴通), J. A. Izaac, Zi-Xi Li (黎子溪), Kai Wang (王凯), Zhao-Zhong Chen (陈召忠), Shining Zhu (祝世宁), J. B. Wang, and Xiao-Song Ma (马小松)
Phys. Rev. Lett. 125, 240501 – Published 8 December 2020
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Abstract

Using quantum walks (QWs) to rank the centrality of nodes in networks, represented by graphs, is advantageous compared to certain widely used classical algorithms. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of a three-, a four-, and a nine-vertex directed graph with parity-time (PT) symmetric quantum walks by using high-dimensional photonic quantum states, multiple concatenated interferometers, and dimension dependent loss to achieve these. We demonstrate the advantage of the QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Furthermore, we extend our experiment from single-photon to two-photon Fock states as inputs and realize the centrality ranking of a nine-vertex graph. Our work shows that a PT symmetric multiphoton quantum walk paves the way for realizing advanced algorithms.

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  • Received 17 December 2019
  • Accepted 28 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.240501

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Tong Wu (吴通)1, J. A. Izaac2, Zi-Xi Li (黎子溪)1, Kai Wang (王凯)1, Zhao-Zhong Chen (陈召忠)1, Shining Zhu (祝世宁)1, J. B. Wang2, and Xiao-Song Ma (马小松)1,*

  • 1National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 2School of Physics, The University of Western Australia, Perth, Western Australia 6009, Australia

  • *Xiaosong.Ma@nju.edu.cn

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Issue

Vol. 125, Iss. 24 — 11 December 2020

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