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Quantum advantage with noisy shallow circuits

Nature Physics volume 16, pages 1040–1045 (2020)Cite this article

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Abstract

As increasingly sophisticated prototypes of quantum computers are being developed, a pressing challenge is to find computational problems that can be solved by an intermediate-scale quantum computer, but are beyond the capabilities of existing classical computers. Previous work in this direction has introduced computational problems that can be solved with certainty by quantum circuits of depth independent of the input size (so-called ‘shallow’ circuits) but cannot be solved with high probability by any shallow classical circuit. Here we show that such a separation in computational power persists even when the shallow quantum circuits are restricted to geometrically local gates in three dimensions and corrupted by noise. We also present a streamlined quantum algorithm that is shown to achieve a quantum advantage in a one-dimensional geometry. The latter may be amenable to experimental implementation with the current generation of quantum computers.

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Fig. 1: A variant of the magic square game21,22.
Fig. 2: Quantum circuit for the 1D Magic Square Problem.
Fig. 3: Encoded 1D Magic Square circuit.

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Acknowledgements

S.B. acknowledges support from the IBM Research Frontiers Institute and funding from the MIT-IBM Watson AI Lab under the project Machine Learning in Hilbert Space. R.K. acknowledges support by the Technical University of Munich—Institute of Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement no. 291763, by the DFG Cluster of Excellence 2111 (Munich Center for Quantum Science and Technology) and by the German Federal Ministry of Education through the funding programme Photonics Research Germany, contract no. 13N14776 (QCDA-QuantERA). D.G. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) under Discovery grant no. RGPIN-2019-04198. D.G. is a CIFAR fellow in the Quantum Information Science Program. D.G. acknowledges research funding from IBM Research. M.T. thanks the Stellenbosch Institute of Advanced Study for hosting him while part of this work was completed.

Author information

Authors and Affiliations

  1. IBM T. J. Watson Research Center, Yorktown Heights, NY, USA

    Sergey Bravyi

  2. Department of Combinatorics and Optimization & Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada

    David Gosset

  3. Institute for Advanced Study & Zentrum Mathematik, Technical University of Munich, Munich, Germany

    Robert König

  4. School of Computer Science & Centre for Quantum Software and Information, University of Technology Sydney, Sydney, New South Wales, Australia

    Marco Tomamichel

  5. Department of Electrical and Computer Engineering & Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore

    Marco Tomamichel

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  1. Sergey Bravyi
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  2. David Gosset
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  3. Robert König
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  4. Marco Tomamichel
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All authors contributed important ideas during initial discussions and contributed equally to deriving the technical proofs and writing the paper.

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Correspondence to Marco Tomamichel.

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Peer review information Nature Physics thanks Stephen Bartlett, Sergio Boixo and Bill Fefferman for their contribution to the peer review of this work.

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Supplementary Information

Proofs of all the results presented in the main text.

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Bravyi, S., Gosset, D., König, R. et al. Quantum advantage with noisy shallow circuits. Nat. Phys. 16, 1040–1045 (2020). https://doi.org/10.1038/s41567-020-0948-z

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