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Published April 11, 2023 | Published
Journal Article Open

Boundaries of quantum supremacy via random circuit sampling


Google's quantum supremacy experiment heralded a transition point where quantum computers can evaluate a computational task, random circuit sampling, faster than classical supercomputers. We examine the constraints on the region of quantum advantage for quantum circuits with a larger number of qubits and gates than experimentally implemented. At near-term gate fidelities, we demonstrate that quantum supremacy is limited to circuits with a qubit count and circuit depth of a few hundred. Larger circuits encounter two distinct boundaries: a return of a classical advantage and practically infeasible quantum runtimes. Decreasing error rates cause the region of a quantum advantage to grow rapidly. At error rates required for early implementations of the surface code, the largest circuit size within the quantum supremacy regime coincides approximately with the smallest circuit size needed to implement error correction. Thus, the boundaries of quantum supremacy may fortuitously coincide with the advent of scalable, error-corrected quantum computing.

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© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. The authors thank Tameem Albash, Fernando Brandão, Elizabeth Crosson, and Maria Spiropulu for discussions, and Johnnie Gray for tensor network simulations of Sycamore circuits. A.Z. and D.A.L. acknowledge support from Caltech's Intelligent Quantum Networks and Technologies (INQNET) research program and by the DOE/HEP QuantISED program grant, Quantum Machine Learning and Quantum Computation Frameworks (QMLQCF) for HEP, award number DE-SC0019227. D.A.L. further acknowledges support from the Oracle Corporation. Contributions. D.A.L. conceived the project. A.Z., B.V., S.B., and D.A.L. wrote the manuscript. A.Z., S.B., and D.A.L. performed the analytic analysis of runtimes. A.Z. implemented the simulations of S.A., and S.F.A., B.V. implemented the simulations of tensor networks. Data availability. We provide all data for computing quantum advantage boundaries in a supplemental GitHub repository. The authors declare no competing interests.

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August 22, 2023
August 22, 2023