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Building a fault-tolerant quantum computer using concatenated cat codes

Chamberland, Christopher and Noh, Kyungjoo and Arrangoiz-Arriola, Patricio and Campbell, Earl T. and Hann, Connor T. and Iverson, Joseph K. and Putterman, Harald and Bohdanowicz, Thomas C. and Flammia, Steven T. and Keller, Andrew J. and Refael, Gil and Preskill, John and Jiang, Liang and Safavi-Naeini, Amir H. and Painter, Oskar and Brandão, Fernando G. S. L. (2022) Building a fault-tolerant quantum computer using concatenated cat codes. PRX Quantum, 3 (1). Art. No. 010329. ISSN 2691-3399. doi:10.1103/PRXQuantum.3.010329.

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We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including cnot and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits, which are currently intractable for classical computers. Hardware with 18 000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Chamberland, Christopher0000-0003-3239-5783
Noh, Kyungjoo0000-0002-6318-8472
Hann, Connor T.0000-0003-0665-7161
Iverson, Joseph K.0000-0003-4665-8839
Putterman, Harald0000-0002-5841-181X
Flammia, Steven T.0000-0002-3975-0226
Keller, Andrew J.0000-0003-3030-1149
Preskill, John0000-0002-2421-4762
Jiang, Liang0000-0002-0000-9342
Safavi-Naeini, Amir H.0000-0001-6176-1274
Painter, Oskar0000-0002-1581-9209
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2022 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 21 December 2020; revised 3 November 2021; accepted 26 January 2022; published 23 February 2022) We thank Qian Xu for helping with the displaced Fock-basis calculation and Alex Retzker for discussions. C.C. thanks Yunong Shi and Pierre-Yves Aquilanti for their help in setting up the AWS clusters where most of the error-correction simulations were performed. We thank all the members of the AWS Center of Quantum Computing for our collaboration on building more powerful quantum technologies. We thank Richard Moulds, Nadia Carlsten, Eric Kessler, and all the members of the Amazon Braket and Quantum Solutions Lab teams. We thank Simone Severini for creating an environment where this research was possible in the first place. We thank Bill Vass, James Hamilton, and Charlie Bell for their support and guidance throughout this project.
Group:Institute for Quantum Information and Matter, AWS Center for Quantum Computing
Issue or Number:1
Record Number:CaltechAUTHORS:20201209-172305164
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107004
Deposited By: Joy Painter
Deposited On:10 Dec 2020 16:40
Last Modified:23 Feb 2022 19:24

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