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Title: Asymmetric quantum Griesmer codes detecting a single bit-flip error
Authors: Luo, Gaojun
Ezerman, Martianus Frederic
Ling, San
Keywords: Science::Mathematics
Issue Date: 2022
Source: Luo, G., Ezerman, M. F. & Ling, S. (2022). Asymmetric quantum Griesmer codes detecting a single bit-flip error. Discrete Mathematics, 345(12), 113088-.
Project: 04INS000047C230GRT01
Journal: Discrete Mathematics
Abstract: The quest to build large-scale quantum computing devices depends on keeping the noise level below a fault-tolerance threshold. In this paper we derive the asymmetric quantum analogue of the Griesmer bound. To benefit from the noise asymmetry in many physical systems, one can decide to only detect a single bit-flip error while maximizing control over the phase-flip errors. We present constructions of such codes via the classical Griesmer codes and obtain infinite families. The optimality of the parameters of the codes in the families is measured against the quantum Griesmer bound. Numerous other codes, which may not be optimal, can also be derived. Choices of their design provide greater flexibility in terms of the resulting quantum parameters. We give examples of good qubit, qutrit, and ququad codes from such a route.
ISSN: 0012-365X
DOI: 10.1016/j.disc.2022.113088
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 Elsevier B.V. All rights reserved. This paper was published in Discrete Mathematics and is made available with permission of Elsevier B.V.
Fulltext Permission: embargo_20240722
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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