Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices

TL;DR

This paper analyzes the performance and mechanisms of QAOA for MaxCut problems, introduces efficient heuristics for parameter optimization, compares it with quantum annealing, and discusses near-term implementation prospects on quantum hardware.

Contribution

It develops a polynomial-time heuristic for QAOA parameter initialization, enhancing its practical performance and provides a realistic resource analysis for near-term quantum device implementations.

Findings

QAOA can exploit non-adiabatic mechanisms to overcome spectral gap issues.

Heuristic initialization strategies significantly reduce optimization complexity.

QAOA implementation on neutral atom systems is feasible for large problem sizes.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood about QAOA's performance beyond its lowest-depth variant. An essential but missing ingredient for understanding and deploying QAOA is a constructive approach to carry out the outer-loop classical optimization. We provide an in-depth study of the performance of QAOA on MaxCut problems by developing an efficient parameter-optimization procedure and revealing its ability to exploit non-adiabatic operations. Building on observed patterns in optimal parameters, we propose heuristic strategies for initializing optimizations to find quasi-optimal $p$-level QAOA parameters in $O(\text{poly}(p))$ time, whereas the standard strategy of random initialization requires $2^{O(p)}$ optimization runs to achieve similar performance. We then benchmark QAOA and compare it with quantum annealing, especially on difficult instances where adiabatic quantum annealing fails due to small spectral gaps. The comparison reveals that QAOA can learn via optimization to utilize non-adiabatic mechanisms to circumvent the challenges associated with vanishing spectral gaps. Finally, we provide a realistic resource analysis on the experimental implementation of QAOA. When quantum fluctuations in measurements are accounted for, we illustrate that optimization will be important only for problem sizes beyond numerical simulations, but accessible on near-term devices. We propose a feasible implementation of large MaxCut problems with a few hundred vertices in a system of 2D neutral atoms, reaching the regime to challenge the best classical algorithms.