Avoiding coherent errors with rotated concatenated stabilizer codes

Abstract

Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an [[n, k, d]] stabilizer outer code with dual-rail inner codes, we obtain a [[2n, k, d]] constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a positive fault-tolerant threshold against stochastic errors. Setting the outer code as a four-qubit amplitude damping code yields an eight-qubit constant-excitation code that corrects a single amplitude damping error, and we analyze this code’s potential as a quantum memory.

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Item Type:	Article
Authors/Creators:	Ouyang, Y. https://orcid.org/0000-0003-1115-0074
Copyright, Publisher and Additional Information:	© The Author(s) 2021. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
Keywords:	quant-ph; quant-ph; cs.IT; math.IT
Dates:	Published: 2 June 2021 Published (online): 2 June 2021 Accepted: 19 April 2021
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield)
Funding Information:	Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/M024261/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/R043825/1
Depositing User:	Symplectic Sheffield
Date Deposited:	25 Jun 2021 11:27
Last Modified:	25 Jun 2021 11:28
Status:	Published
Publisher:	Springer Science and Business Media LLC
Refereed:	Yes
Identification Number:	10.1038/s41534-021-00429-8
Related URLs:	arXiv URL
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:175245

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Avoiding coherent errors with rotated concatenated stabilizer codes

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