Optimization Performance of QA and QAOA

This white paper surveys the research literature on quantum optimization solvers, specifically comparing the quantum annealing (QA) method implemented by D-Wave with the quantum approximate optimization algorithm (QAOA) that operates on gate-model quantum platforms. The document outlines empirical tests that demonstrate QA significantly outperforms QAOA on current-generation quantum processors. It details the methodologies of both approaches, highlighting that QA is implemented on specialized quantum hardware, while QAOA runs on general-purpose quantum systems. The paper presents empirical comparisons from various studies, indicating that QA consistently returns better solutions than QAOA across different problem sizes. Furthermore, it discusses theoretical challenges that QAOA faces, suggesting that it may never be competitive with QA, even on future error-corrected quantum platforms. The findings underscore the advantages of D-Wave's QA technology in solving combinatorial optimization problems effectively.