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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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).
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Nature Physics (2018)