Quantum Simulation of Perfect State Transfer on Weighted Cubelike Graphs

A continuous-time quantum walk on a graph evolves according to the unitary operator e(-i At), where A is the adjacency matrix of the graph. Perfect state transfer (PST) in a quantum walk is the transfer of a quantum state from one node of a graph to another node with 100% fidelity. It can be shown that the adjacency matrix of a cubelike graph is a finite sum of tensor products of Pauli X operators. We use this fact to construct an efficient quantum circuit for the quantum walk on cubelike graphs. In [5, 15], a characterization of integer weighted cubelike graphs is given that exhibit periodicity or PST at time t = pi/2. We use our circuits to demonstrate PST or periodicity in these graphs on IBM's quantum computing platform [1, 10].