Design of quantum error correcting code for biased error on heavy-hexagon structureopen access
- Authors
- Kim, Younghun; Kang, Jeongsoo; Kwon, Younghun
- Issue Date
- Jun-2023
- Publisher
- Kluwer Academic Publishers
- Citation
- Quantum Information Processing, v.22, no.230, pp.1 - 16
- Indexed
- SCIE
SCOPUS
- Journal Title
- Quantum Information Processing
- Volume
- 22
- Number
- 230
- Start Page
- 1
- End Page
- 16
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/188185
- DOI
- 10.1007/s11128-023-03979-2
- ISSN
- 1570-0755
- Abstract
- Surface code is an error-correcting method that can be applied to the implementation of a usable quantum computer. At present, a promising candidate for a usable quantum computer is based on superconductor-specifically transmon. Because errors in transmon-based quantum computers appear biasedly as Z type errors, tailored surface and XZZX codes have been developed to deal with the type errors. Even though these surface codes have been suggested for lattice structures, since transmons-based quantum computers, developed by IBM, have a heavy-hexagon structure, it is natural to ask how tailored surface code and XZZX code can be implemented on the heavy-hexagon structure. In this study, we provide a method for implementing tailored surface code and XZZX code on a heavy-hexagon structure. Even when there is no bias, we obtain 0.231 % as the threshold of the tailored surface code, which is much better than 0.21 % and 0.209 % as the thresholds of the surface code and XZZX code, respectively. Furthermore, we can see that even though a decoder, which is not the best of the syndromes, is used, the thresholds of the tailored surface code and XZZX code increase as the bias of the Z error increases. Finally, we show that in the case of infinite bias, the threshold of the surface code is 0.264 % , but the thresholds of the tailored surface code and XZZX code are 0.296 % and 0.328 % respectively. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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