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Evidence for quantum annealing with more than one hundred qubits

Nature Physics volume 10, pages 218–224 (2014)Cite this article

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Abstract

Quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators may be built with capabilities exceeding classical computers. A quantum annealer, in particular, solves optimization problems by evolving a known initial configuration at non-zero temperature towards the ground state of a Hamiltonian encoding a given problem. Here, we present results from tests on a 108 qubit D-Wave One device based on superconducting flux qubits. By studying correlations we find that the device performance is inconsistent with classical annealing or that it is governed by classical spin dynamics. In contrast, we find that the device correlates well with simulated quantum annealing. We find further evidence for quantum annealing in the form of small-gap avoided level crossings characterizing the hard problems. To assess the computational power of the device we compare it against optimized classical algorithms.

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Figure 1: Success probability distributions.
Figure 2: Correlations.
Figure 3: Correlations of gauge-averaged data.
Figure 4: Evolution of the lowest spectral gap.
Figure 5: Correlation of success probability and the Hamming distance from excited states to the nearest ground state.
Figure 6: Scaling with problem size.

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Acknowledgements

We acknowledge useful discussions with M. H. Amin, M. H. Freedman, H. G. Katzgraber, C. Marcus, B. Smith and K. Svore. We thank L. Wang for providing data of spin dynamics simulations, G. Wagenbreth for help in optimizing the belief propagation code and P. Messmer for help in optimizing the GPU codes. We are grateful to J. Smolin and G. Smith for suggesting that we test classical spin dynamics. Simulations were performed on the Brutus cluster at ETH Zurich and on computing resources of Microsoft Research with the help of J. Jernigan. This work was supported by the Swiss National Science Foundation through the NCCR QSIT, by ARO grant number W911NF-12-1-0523, by ARO MURI grant number W911NF-11-1-0268, by Lockheed Martin Corporation, by DARPA grant number FA8750-13-2-0035, and by NSF grant number CHE-1037992. MT acknowledges the hospitality of the Aspen Center for Physics, supported by NSF grant PHY-1066293. The initial planning of the tests by MT was funded by Microsoft Research.

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Authors and Affiliations

  1. Information Sciences Institute and Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA

    Sergio Boixo

  2. Theoretische Physik, ETH Zurich, 8093 Zürich, Switzerland

    Troels F. Rønnow, Sergei V. Isakov & Matthias Troyer

  3. Department of Chemistry and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA

    Zhihui Wang

  4. Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA

    David Wecker

  5. Department of Electrical Engineering, Chemistry and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA

    Daniel A. Lidar

  6. Department of Physics, University of California, Santa Barbara, California 93106-9530, USA

    John M. Martinis

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  1. Sergio Boixo
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  8. Matthias Troyer
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Contributions

M.T., J.M.M. and D.A.L. designed the tests and wrote the manuscript, with input from all other authors. S.B. and Z.W. performed the tests on D-Wave One. S.V.I., T.F.R. and M.T. wrote the simulated classical and quantum annealing codes and T.F.R., S.V.I., M.T. and D.W. performed the simulations. S.B. and T.F.R. wrote the bucket sort code and the divide-and-conquer codes. T.F.R., S.V.I., M.T., S.B., Z.W. and D.A.L. evaluated the data. All authors contributed to the discussion and presentation of the results.

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Correspondence to Matthias Troyer.

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The authors declare no competing financial interests.

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Boixo, S., Rønnow, T., Isakov, S. et al. Evidence for quantum annealing with more than one hundred qubits. Nature Phys 10, 218–224 (2014). https://doi.org/10.1038/nphys2900

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