近日，国防科技大学徐平团队实现了利用辅助克服有向图中心性排序的叠加状态限制。相关论文于2025年7月21日发表在《物理评论A》杂志上。

研究组提供了一个有向图中心性排序的量子行走算法的片上实验演示。他们提出了一种有向图中心性排序算法，称为辅助伪厄米连续时间量子行走算法（AA-PHCTQW）。AA-PHCTQW克服了现有的基于CTQW的中心性排序算法的一个常见限制，无论是对于无向图还是有向图，这都是对所有顶点均匀叠加的初始状态的要求。

利用辅助顶点，研究组使单顶点基状态的主题作为初始系统状态，从而显著提高了算法的实验可行性和抗噪声性。他们证明了AA-PHCTQW的正确性，并分析了PHCTQW和AA-PHCTQW在随机图上的中心性度量。此外，研究组还在硅基可重构光子芯片上对该算法进行了实验验证，该芯片具有前置的单光子存在和多光子存在，完成了三节点和九节点有向图的AA-PHCTQW。

附：英文原文

Title: Overcoming the superposition-state limitation for directed graph centrality ranking with ancilla assistance

Author: Miaomiao Yu, Pingyu Zhu, Yang Wang, Yan Wang, Yuxing Du, Kun Wang, Ping Xu

Issue&Volume: 2025/07/21

Abstract: We propose an algorithm for directed graph centrality ranking, called the ancilla-assisted pseudo-Hermitian continuous-time quantum walk algorithm (AA-PHCTQW). AA-PHCTQW overcomes a common limitation for existing CTQW-based centrality ranking algorithms, both for undirected and directed graphs, which is the requirement of an initial state in a uniform superposition over all vertices. Leveraging an ancilla vertex, we enable the use of a single-vertex basis state as the initial system state, thereby significantly improving the algorithm's experimental feasibility and robustness against noise. We prove the correctness of AA-PHCTQW and analyze centrality measures from PHCTQW and AA-PHCTQW on random graphs. Furthermore, we experimentally validate the algorithm on a silicon-based reconfigurable photonic chip with heralded single-photon source and multiphoton sources, complete the AA-PHCTQW of three-node and nine-node directed graphs. Here we provide an on-chip experimental demonstration of a quantum walk algorithm for directed graph centrality ranking.

DOI: 10.1103/sv7q-gknn

Source: https://journals.aps.org/pra/abstract/10.1103/sv7q-gknn