Quantum imaginary time evolution and UD-MIS problem

TL;DR

This paper applies quantum imaginary time evolution to solve the unit-disk maximum independent set problem, demonstrating low failure probabilities that decrease with more shots and providing a theoretical failure bound.

Contribution

The work introduces a quantum imaginary time evolution approach for the UD-MIS problem, with numerical validation and a new theoretical failure probability bound.

Findings

Failure probability decreases rapidly with more shots.

Numerical simulations for 6, 8, and 10-qubit graphs show small failure rates.

A theoretical upper bound for failure probability was derived.

Abstract

In this work we apply a procedure based on the quantum imaginary time evolution method to solve the unit-disk maximum independent set problem. Numerical simulations were performed for instances of 6, 8 and 10-qubits graphs. We have found that the failure probability of the procedure is relatively small and rapidly decreases with the number of shots. In addition, a theoretical upper bound for the failure probability of the procedure was obtained.