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.

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• Quantum algorithms & computation