Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems

TL;DR

This paper introduces pVSQA, a hybrid quantum-classical algorithm that optimizes solutions for constrained combinatorial problems using variational schedules and post-processing, demonstrated on quantum hardware.

Contribution

It presents a novel hybrid quantum algorithm combining variational scheduling and post-processing for constrained COPs, applicable to quantum annealers and gate devices.

Findings

pVSQA achieves near-optimal solutions with few parameters on simulators.

The method effectively satisfies constraints via post-processing.

Experimental results on quantum hardware validate the approach.

Abstract

We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a quantum annealer or gate-type quantum device. Variational methods are used to find an optimal schedule function that leads to high-quality solutions in a short amount of time. Post-processing techniques convert the output solutions of the quantum devices to satisfy the constraints of the COPs. pVSQA combines the variational methods and the post-processing technique. We obtain a sufficient condition for constrained COPs to apply pVSQA based on a greedy post-processing algorithm. We apply the proposed method to two constrained NP-hard COPs: the graph partitioning problem and the quadratic knapsack problem. pVSQA on a simulator shows that a small number of variational parameters is sufficient to achieve a (near-)optimal performance within a predetermined operation time. Then building upon the simulator results, we implement pVSQA on a quantum annealer and a gate-type quantum device. The experimental results demonstrate the effectiveness of our proposed method.