Multiscale Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an active area of research to exhibit its speedup over classical algorithms. The performance of the QAOA at low depths is limited, while the QAOA at higher depths is constrained by the current techniques. We propose a new version of QAOA that incorporates the capabilities of QAOA and the real-space renormalization group transformation, resulting in enhanced performance. Numerical simulations demonstrate that our algorithm can provide accurate solutions for certain randomly generated instances utilizing QAOA at low depths, even at the lowest depth. The algorithm is suitable for NISQ devices to exhibit a quantum advantage.