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Overhead analysis of universal concatenated quantum codes

Chamberland, Christopher and Jochym-O'Connor, Tomas and Laflamme, Raymond (2017) Overhead analysis of universal concatenated quantum codes. Physical Review A, 95 (2). Art. No. 022313. ISSN 2469-9926. doi:10.1103/PhysRevA.95.022313.

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We analyze the resource overhead of recently proposed methods for universal fault-tolerant quantum computation using concatenated codes. Namely, we examine the concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code, which allows for the construction of the 49- and 105-qubit codes that do not require the need for magic state distillation for universality. We compute a lower bound for the adversarial noise threshold of the 105-qubit code and find it to be 8.33 × 10(−6). We obtain a depolarizing noise threshold for the 49-qubit code of 9.69 × 10(−4) which is competitive with the 105-qubit threshold result of 1.28 × 10^(−3). We then provide lower bounds on the resource requirements of the 49- and 105-qubit codes and compare them with the surface code implementation of a logical T gate using magic state distillation. For the sampled input error rates and noise model, we find that the surface code achieves a smaller overhead compared to our concatenated schemes.

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Additional Information:© 2017 American Physical Society. (Received 27 September 2016; published 8 February 2017; corrected 15 February 2017) T.J. would like to acknowledge the support of NSERC and the Vanier-Banting Secretariat through the Vanier CGS. C.C. would like to acknowledge the support of QEII-GSST and to thank S. Weiss for providing the necessary computational resources. This work was supported by CIFAR, NSERC, and Industry Canada.
Errata:This paper was published online on 8 February 2017 with an omission of an author affiliation and incorrect sizing of Fig. 5. Tomas Jochym-O’Connor’s additional affiliation should read as “2Walter Burke Institute for Theoretical Physics and Institute for Quantum Information & Matter, California Institute of Technology, Pasadena, California 91125, USA.” Figure 5 has been resized and the additional author affiliation has been added as of 15 February 2017. The figure is correct and the author affiliation is present in the printed version of the journal.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Vanier-Banting SecretariatUNSPECIFIED
Queen Elizabeth II Graduate Scholarships in Science & TechnologyUNSPECIFIED
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Industry CanadaUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20170215-085450346
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Official Citation:Christopher Chamberland, Tomas Jochym-O'Connor, and Raymond Laflamme Phys. Rev. A 95, 022313
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74315
Deposited By: George Porter
Deposited On:15 Feb 2017 18:22
Last Modified:11 Nov 2021 05:26

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