Benchmarking quantum annealing with maximum cardinality matching problems

Frontiers in Computer Science, vol. 6

Abstract

We benchmark Quantum Annealing (QA) vs. 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 especially 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.

Authors 6

1. Daniel Vert

   Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Laboratoire d'Intégration des Systèmes et des Technologies

   Affiliation as printed

   AIDAS, Palaiseau, France

   Université Paris-Saclay Commission for Atomic Energy (CEA), Laboratory of Integration of Systems and Technologies (LIST), Palaiseau, France

2. Madita Willsch Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

   University in German Rheinisch-Westfälische Technische Hochschule Aachen (RWTH), Jülich, Germany

3. Berat Yenilen Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

   RWTH Aachen University, Aachen, Germany

4. Renaud Sirdey

   Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Laboratoire d'Intégration des Systèmes et des Technologies

   Affiliation as printed

   AIDAS, Palaiseau, France

   Université Paris-Saclay Commission for Atomic Energy (CEA), Laboratory of Integration of Systems and Technologies (LIST), Palaiseau, France

5. Stéphane Louise corresponding

   Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Laboratoire d'Intégration des Systèmes et des Technologies

   Affiliation as printed

   AIDAS, Palaiseau, France

   Université Paris-Saclay Commission for Atomic Energy (CEA), Laboratory of Integration of Systems and Technologies (LIST), Palaiseau, France

6. Kristel F. L. Michielsen corresponding Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

   RWTH Aachen University, Aachen, Germany

   University in German Rheinisch-Westfälische Technische Hochschule Aachen (RWTH), Jülich, Germany