Abstract

A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of supercomputers. Such a demonstration of what is referred to as quantum supremacy requires a reliable evaluation of the resources required to solve tasks with classical approaches. Here, we propose the task of sampling from the output distribution of random quantum circuits as a demonstration of quantum supremacy. We extend previous results in computational complexity to argue that this sampling task must take exponential time in a classical computer. We introduce cross-entropy benchmarking to obtain the experimental fidelity of complex multiqubit dynamics. This can be estimated and extrapolated to give a success metric for a quantum supremacy demonstration. We study the computational cost of relevant classical algorithms and conclude that quantum supremacy can be achieved with circuits in a two-dimensional lattice of 7 × 7 qubits and around 40 clock cycles. This requires an error rate of around 0.5% for two-qubit gates (0.05% for one-qubit gates), and it would demonstrate the basic building blocks for a fault-tolerant quantum computer.

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Acknowledgements

We especially acknowledge M. Smelyanskiy, from the Parallel Computing Laboratory, Intel Corporation, who performed the simulations of circuits with 6 × 6 and 7 × 6 qubits and wrote the corresponding section in the Supplementary Information. We would like to acknowledge A. Montanaro for multiple suggestions, especially regarding IQP circuits. We would like to thank S. Aaronson, A. Fowler, I. Markov, M. Mohseni and E. Rieffel for discussions. The authors also thank J. Hammond, from the Parallel Computing Laboratory, Intel Corporation, for his useful insights into MPI run-time performance and scalability. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under contract no. DEAC02-05CH11231. M.J.B. has received financial support from the Australian Research Council via the Future Fellowship scheme (project no. FT110101044) and as a member of the ARC Centre of Excellence for Quantum Computation and Communication Technology (project no. CE170100012).

Author information

Affiliations

  1. Google Inc., Venice, CA, USA

    • Sergio Boixo
    • , Vadim N. Smelyanskiy
    • , Ryan Babbush
    • , Nan Ding
    •  & Hartmut Neven
  2. Google Inc., Zurich, Switzerland

    • Sergei V. Isakov
  3. QuAIL, NASA Ames Research Center, Moffett Field, CA, USA

    • Zhang Jiang
  4. SGT Inc., Greenbelt, MD, USA

    • Zhang Jiang
  5. Centre for Quantum Computation and Communication Technology, Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, New South Wales, Australia

    • Michael J. Bremner
  6. Google Inc., Santa Barbara, CA, USA

    • John M. Martinis
  7. Department of Physics, University of California, Santa Barbara, CA, USA

    • John M. Martinis

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Contributions

S.B. designed the project. S.B. and V.N.S. developed most of the theory. S.V.I. performed numerical studies and designed the specific quantum circuits. All authors contributed to several tasks, such as analysis of theory and results and discussions of the draft.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Sergio Boixo.

Supplementary information

  1. Supplementary Information

    Supplementary notes, Supplementary Figures, Supplementary references

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https://doi.org/10.1038/s41567-018-0124-x

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