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Algorithmics"],"published-print":{"date-parts":[[2021,12,31]]},"abstract":"<jats:p>Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs. We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these approaches for comparing our solution values to those obtained on the current quantum annealing machine, D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware. In addition, we also evaluate the performance of a heuristic by Selby. It has been a matter of discussion in the literature how well the D-Wave hardware performs at its native task, and our experiments shed some more light on this issue. In particular, we examine how reliably the D-Wave computer can deliver true optimum solutions and present some surprising results.<\/jats:p>","DOI":"10.1145\/3459606","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T15:06:22Z","timestamp":1625843182000},"page":"1-30","source":"Crossref","is-referenced-by-count":32,"title":["Quantum Annealing versus Digital Computing"],"prefix":"10.1145","volume":"26","author":[{"given":"Michael","family":"J\u00fcnger","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Cologne, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elisabeth","family":"Lobe","sequence":"additional","affiliation":[{"name":"DLR German Aerospace Center, Braunschweig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Petra","family":"Mutzel","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Bonn, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gerhard","family":"Reinelt","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Heidelberg University, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Franz","family":"Rendl","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Klagenfurt, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanni","family":"Rinaldi","sequence":"additional","affiliation":[{"name":"Istituto di Analisi dei Sistemi ed Informatica \u201cA. 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