Design of Quantum error correcting code for biased error on
heavy-hexagon structure
- URL: http://arxiv.org/abs/2211.14038v1
- Date: Fri, 25 Nov 2022 11:29:50 GMT
- Title: Design of Quantum error correcting code for biased error on
heavy-hexagon structure
- Authors: Younghun Kim, Jeongsoo Kang and Younghun Kwon
- Abstract summary: We provide a method for implementing tailored surface code and XZZX code on a heavy-hexagon structure.
In the case of infinite bias, the threshold of the surface code is $ 0.264852%$, but the thresholds of the tailored surface code and XZZX code are $ 0.296157 % $ and $ 0.328127%$ respectively.
- Score: 2.1485350418225244
- License: http://creativecommons.org/licenses/by/4.0/
- 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 $ 0.231779 \%$
as the threshold of the tailored surface code, which is much better than $
0.210064 \%$ and $ 0.209214 \%$ 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 $ 0.264852\%$, but the thresholds of the tailored surface code
and XZZX code are $ 0.296157 \% $ and $ 0.328127 \%$ respectively.
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