Experimental parity-time symmetry quantum walks on a directed graph

TL;DR

This paper demonstrates the experimental realization of parity-time symmetric quantum walks on directed graphs using photonic states, showing advantages in network analysis tasks like breaking vertex rank degeneracy.

Contribution

It introduces a method to implement PT-symmetric quantum walks on directed graphs, overcoming previous challenges with non-Hermitian Hamiltonians.

Findings

Successfully implemented PT-symmetric quantum walks on 3- and 4-vertex directed graphs.

Demonstrated breaking of vertex rank degeneracy in a 4-vertex graph.

Showed potential for advanced quantum network algorithms.

Abstract

Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of nodes in networks represented by graphs. Employing QW in centrality ranking is advantageous comparing to certain widely used classical algorithms (e.g. PageRank) because QW approach can lift the vertex rank degeneracy in certain graphs. 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 both a three-vertex and four-vertex directed graphs with parity-time (PT) symmetric quantum walks. To achieve this, we use high-dimensional photonic quantum states, optical circuitries consisting of multiple concatenated interferometers and dimension dependent loss. Importantly, we demonstrate the advantage of QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Our work shows that PT-symmetric quantum walks may be useful for realizing advanced algorithm in a quantum network.