Quantum simulation of perfect state transfer on weighted cubelike graphs

TL;DR

This paper develops quantum circuits for simulating perfect state transfer on weighted cubelike graphs and demonstrates their effectiveness on IBM quantum hardware, advancing quantum communication protocols.

Contribution

It introduces an efficient quantum circuit construction for walks on cubelike graphs and experimentally verifies PST and periodicity on real quantum computers.

Findings

Successfully demonstrated PST on IBM quantum hardware.

Provided a new circuit-based approach for simulating quantum walks on cubelike graphs.

Confirmed periodicity and PST in weighted cubelike graphs at specific times.

Abstract

A continuous-time quantum walk on a graph evolves according to the unitary operator $e^{-iAt}$, 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 \cite{Cao2021, rishi2021(2)}, 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~\cite{Qiskit, IBM2021}.