Design and Analysis of an Improved Constrained Hypercube Mixer in Quantum Approximate Optimization Algorithm

TL;DR

This paper improves the hypercube mixer in QAOA to better handle constrained problems, reducing circuit complexity and enhancing noise robustness, thus advancing practical quantum optimization in NISQ devices.

Contribution

It introduces a modified hypercube mixer that generates fewer gates for linear constrained problems and provides an analytical bound on its applicability.

Findings

Reduced circuit size improves noise robustness.

Numerical results show enhanced QAOA performance.

Analytical bounds define problem size limits.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is expected to offer advantages over classical approaches when solving combinatorial optimization problems in the Noisy Intermediate-Scale Quantum (NISQ) era. In its standard formulation, however, QAOA is not suited for constrained problems. One way to incorporate certain types of constraints is to restrict the mixing operator to the feasible subspace; however, this substantially increases circuit size, thereby reducing noise robustness. In this work, we refine an existing hypercube mixer method for enforcing hard constraints in QAOA. We present a modification that generates circuits with fewer gates for a broad class of constrained problems defined by linear functions. Furthermore, we calculate an analytical upper bound on the number of binary variables for which this reduction might not apply. Additionally, we present numerical experimental results demonstrating that the proposed approach improves robustness to noise. In summary, the method proposed in this paper allows for more accurate QAOA performance in noisy settings, bringing us closer to practical, real-world NISQ-era applications.