Building a fault-tolerant quantum computer using concatenated cat codes

• URL: http://arxiv.org/abs/2012.04108v2
• Date: Thu, 27 Jan 2022 08:21:04 GMT
• Title: Building a fault-tolerant quantum computer using concatenated cat codes
• Authors: Christopher Chamberland, Kyungjoo Noh, Patricio Arrangoiz-Arriola, Earl T. Campbell, Connor T. Hann, Joseph Iverson, Harald Putterman, Thomas C. Bohdanowicz, Steven T. Flammia, Andrew Keller, Gil Refael, John Preskill, Liang Jiang, Amir H. Safavi-Naeini, Oskar Painter, Fernando G.S.L. Brand\~ao
• Abstract summary: We present a proposed fault-tolerant quantum computer based on cat codes with outer quantum error-correcting codes. We numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer.
• Score: 44.03171880260564
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 1,000 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.

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