Quantum Local Search with the Quantum Alternating Operator Ansatz

Abstract

We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. The quantum local search algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We compare the performance of this algorithm on 3-regular graphs with up to 100 nodes against the well known classical Boppana-Halldórsson algorithm for the Maximum Independent Set problem.

Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation

“…The quantum-classical variational algorithm presented in this work utilized the dynamic quantum variational ansatz (DQVA) to perform the constrained optimization on each of the subgraphs produced by the partition. Recently, a quantum local search algorithm has been proposed, also targeting the MIS problem, which tackles large graphs using a fixed allocation of quantum resources [13]. The goal of both of these works is scaling up the ability of hybrid variational algorithms to target larger problem instances.…”

“…However, DQVA is not the only approach to solving constrained optimization problems. We could have also used quantum local search which was recently demonstrated to efficiently find approximate solutions to the MIS problem on large graph instances [13].…”