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

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.