Quantum Optimization Heuristics with an Application to Knapsack Problems

TL;DR

This paper enhances the Quantum Approximate Optimization Algorithm (QAOA) for constrained problems by integrating classical greedy solutions and avoiding local minima, demonstrating improved performance on knapsack problem instances.

Contribution

It introduces two novel techniques to adapt QAOA for constrained optimization, leveraging classical solutions and local minima avoidance strategies.

Findings

Adjusted quantum heuristics outperform classical heuristics on knapsack instances.

Techniques improve quantum algorithm's ability to explore around greedy solutions.

Results obtained with unit depth quantum circuits.

Abstract

This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the local minima around the greedy solutions. To analyze the benefits of these two techniques we run the quantum algorithm on known hard instances of the Knapsack Problem using unit depth quantum circuits. The results show that the adjusted quantum optimization heuristics typically perform better than various classical heuristics.