Compressed space quantum approximate optimization algorithm for constrained combinatorial optimization

TL;DR

This paper introduces a compressed space approach for QAOA that efficiently handles constraints in combinatorial optimization problems by reducing qubit requirements and maintaining solution quality, demonstrated through quantum simulator experiments.

Contribution

It presents a scalable method to engineer a compressed feasible solution space and integrates it with QAOA for constrained COPs, addressing limitations of existing techniques.

Findings

Effective reduction of qubits needed for constrained COPs

Successful demonstration on quantum simulator

Improved handling of constraints in QAOA

Abstract

Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of combinatorial optimization problems (COPs). However, effectively dealing with constraints of COPs remains a significant challenge. Existing methods, such as tailoring mixing operators, are typically limited to specific constraint types, like one-hot constraints. To address these limitations, we introduce a method for engineering a compressed space that represents the feasible solution space with fewer qubits than the original. Our approach includes a scalable technique for determining the unitary transformation between the compressed and original spaces on gate-based quantum computers. We then propose compressed space QAOA, which seeks near-optimal solutions within this reduced space, while utilizing the Ising model formulated in the original Hilbert space. Experimental results on a quantum simulator demonstrate the effectiveness of our method in solving various constrained COPs.