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.
@article{arxiv.2108.08805,
title = {Quantum Optimization Heuristics with an Application to Knapsack Problems},
author = {Wim van Dam and Karim Eldefrawy and Nicholas Genise and Natalie Parham},
journal= {arXiv preprint arXiv:2108.08805},
year = {2022}
}
Comments
21 pages. v2 fixed typo in Eqs 19 and 35, and in Algorithm 8 pseudocode