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arXiv · 1502.01663

Probing for quantum speedup in spin glass problems with planted solutions

Itay Hen·Joshua Job·Tameem Albash·Troels F. Rønnow·Matthias Troyer·Daniel Lidar
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Abstract

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

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Itay Hen, Joshua Job, Tameem Albash, Troels F. Rønnow, Matthias Troyer, Daniel Lidar. 2015-02-05. Probing for quantum speedup in spin glass problems with planted solutions. https://doi.org/10.1103/physreva.92.042325

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