Benchmarking Quantum Annealing with Maximum Cardinality Matching Problems Provisionally Accepted

Daniel Vert^{1, 2, 3} Madita Willsch^{4, 5*} Berat Yenilen^{4, 6} Renaud Sirdey^{1, 2, 3} Stéphane Louise^{1, 2, 3*} Kristel Michielsen^{4, 5, 6*}

• ¹CEA Saclay, France
• ²Université Paris-Saclay, France
• ³AIDAS, France
• ⁴Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany
• ⁵AIDAS, Germany
• ⁶RWTH Aachen University, Germany

We benchmark Quantum Annealing (QA) versus Simulated Annealing (SA) with a focus on the impact of the embedding of problems onto the different topologies of the D-Wave quantum annealers. The series of problems we study are specially designed instances of the maximum cardinality matching problem that are easy to solve classically but difficult for SA and, as found experimentally, not easy for QA either. In addition to using several D-Wave processors, we simulate the QA process by numerically solving the time-dependent Schrödinger equation. We find that the embedded problems can be significantly more difficult than the unembedded problems, and some parameters, such as the chain strength, can be very impactful for finding the optimal solution. Thus, finding a good embedding and optimal parameter values can improve the results considerably. Interestingly, we find that although SA succeeds for the unembedded problems, the SA results obtained for the embedded version scale quite poorly in comparison with what we can achieve on the D-Wave quantum annealers.