Proposal for implementing quantum walks on multidimensional networks

Discrete-time quantum walks (DTQWs) have broad applications in quantum computation and simulation, particularly in universal quantum computing. Prior research in circuit quantum electrodynamics (QED) has focused on implementing DTQWs in one-dimensional chains. However, to achieve practical quantum tasks, it is crucial to extend DTQWs to multidimensional networks with diverse structures. Here, we propose a protocol for realizing DTQWs in multidimensional networks, which accommodate nodes with different numbers of neighbors. Using this protocol, we numerically simulate a Grover walk search algorithm in a cubic network with circuit QED. Our simulations, which consider decoherence, align well with theoretical predictions. Our universal protocol can be adapted for various quantum systems and paves the way for DTQWs in multidimensional networks, which has potential applications in quantum computing and simulation.