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Error suppression via complementary gauge choices in Reed-Muller codes

Chamberland, Christopher and Jochym-O’Connor, Tomas (2017) Error suppression via complementary gauge choices in Reed-Muller codes. Quantum Science and Technology, 2 (3). Art. No. 035008. ISSN 2058-9565. doi:10.1088/2058-9565/aa7c4a.

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Concatenation of two quantum error-correcting codes with complementary sets of transversal gates can provide a means toward universal fault-tolerant quantum computation. We first show that it is generally preferable to choose the inner code with the higher pseudo-threshold to achieve lower logical failure rates. We then explore the threshold properties of a wide range of concatenation schemes. Notably, we demonstrate that the concatenation of complementary sets of Reed-Muller codes can increase the code capacity threshold under depolarizing noise when compared to extensions of previously proposed concatenation models. We also analyze the properties of logical errors under circuit-level noise, showing that smaller codes perform better for all sampled physical error rates. Our work provides new insights into the performance of universal concatenated quantum codes for both code capacity and circuit-level noise.

Item Type:Article
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Additional Information:© 2017 IOP Publishing Ltd. Received 5 May 2017; Accepted 28 June 2017; Accepted Manuscript online 28 June 2017; Published 2 August 2017. The authors thank Joel Wallman for useful discussions and Steve Weiss for providing the necessary computational resources. CC would like to acknowledge the support of QEII-GSST. TJ would like to acknowledge the support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Queen Elizabeth II Graduate Scholarships in Science & Technology (QEII-GSST)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:quantum error correction, fault-tolerant quantum computing, universal quantum codes
Issue or Number:3
Record Number:CaltechAUTHORS:20170802-091844739
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Official Citation:Christopher Chamberland and Tomas Jochym-O'Connor 2017 Quantum Sci. Technol. 2 035008
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79744
Deposited By: Tony Diaz
Deposited On:02 Aug 2017 17:23
Last Modified:15 Nov 2021 17:50

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