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Optimal Bacon-Shor codes

Napp, John and Preskill, John (2013) Optimal Bacon-Shor codes. Quantum Information and Computation, 13 (5-6). pp. 490-510. ISSN 1533-7146. doi:10.48550/arXiv.1209.0794v1.

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We study the performance of Bacon-Shor codes, quantum subsystem codes which are well suited for applications to fault-tolerant quantum memory because the error syndrome can be extracted by performing two-qubit measurements. Assuming independent noise, we find the optimal block size in terms of the bit-flip error probability pX and the phase error probability pZ, and determine how the probability of a logical error depends on pX and pZ. We show that a single Bacon-Shor code block, used by itself without concatenation, can provide very effective protection against logical errors if the noise is highly biased (pZ/pX ≫1) and the physical error rate pZ is a few percent or below. We also derive an upper bound on the logical error rate for the case where the syndrome data is noisy.

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Additional Information:© 2013 Rinton Press. Received September 6, 2012. Revised December 21, 2012. We thank Peter Brooks and Franz Sauer for valuable discussions. This work was supported in part by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center contract number D11PC20165. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC or the U.S. Government. We also acknowledge support from NSF grant PHY-0803371, DOE grant DE-FG03-92-ER40701, NSA/ARO grant W911NF-09-1-0442, Caltech’s Summer Undergraduate Research Fellowship (SURF) program, and the Victor Neher SURF Endowment. The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation.
Group:Institute for Quantum Information and Matter, Caltech Theory
Funding AgencyGrant Number
Intelligence Advanced Research Projects Activity (IARPA)UNSPECIFIED
Department of Interior National Business CenterD11PC20165
Department of Energy (DOE)DE-FG03-92-ER40701
National Security Agency (NSA)/Army Research Office (ARO)W911NF-09-1-0442
Caltech Summer Undergraduate Research Fellowship (SURF) ProgramUNSPECIFIED
Victor Neher SURF EndowmentUNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:Quantum error correction
Issue or Number:5-6
Record Number:CaltechAUTHORS:20130325-085516990
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Official Citation:Napp, John and Preskill, John (2013) Optimal Bacon-Shor codes. Quantum Information and Computation, 13 (5-6). pp. 490-510. ISSN 1533-7146
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37606
Deposited By: Tony Diaz
Deposited On:10 May 2013 16:57
Last Modified:02 Jun 2023 00:15

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