Supervised graph classification for chiral quantum walks

Abstract

Particle transport in quantum systems, which can be modeled by quantum walks on graphs, demonstrates a faster propagation advantage over the corresponding transport in classical systems. As known from several graph examples, achieving further advantages is possible by adding directional control in quantum walks. One way to introduce directional bias is via time-reversal symmetry breaking that can be achieved with chiral quantum walks, where complex phases are added to the edge weights. However, it is not known for which complex phases values and on which graphs quantum transport can be enhanced. Therefore, the classification of graph properties remains an open problem. Here we tackle this graph classification problem with a graph convolutional neural network trained on a set of simulated examples. We find that chiral quantum-walk dynamics leads to almost always faster transport on hypercubes compared to nonchiral dynamics. We connect our paper to physical implementations of quantum walks in superconducting qubits and optical waveguides. Our results open the possibility and flexibility of experimental implementations in demonstrating quantum-walk advantage.