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Yoked surface code[1]

Description

Member of a family of \([[n,k,d]]\) qubit CSS codes resulting from a concatenation of a QMDPC code with a rotated surface code. Concatenation does not impose additional connectivity constraints and can as much as triple the number of logical qubits per physical qubit when compared to the original surface code. Concatenation with 1D (2D) QMDPC yields codes with twice (four times) the distance. The stabilizer generators of the outer QMDPC code are referred to as yokes in this context.

Decoding

Soft information from the inner surface codes can be utilized via a message passing algorithm [2].Yokes can be measured using lattice surgery [1].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Parents
Qubit CSS code
Quantum LDPC (QLDPC) codeStabilizer Hamiltonian-based QECC Quantum
Concatenated qubit codeQubit Concatenated quantum QECC Quantum
A yoked surface code is a concatenation of a QMDPC code (outer code) with a rotated surface code (inner code).
Yoked surface code
Children
Quantum multi-dimensional parity-check (QMDPC) code
Yoked surface codes are concatenations of QMDPC codes with rotated surface codes.
Rotated surface code
Yoked surface codes are concatenations of QMDPC codes with rotated surface codes.

References

[1]
C. Gidney, M. Newman, P. Brooks, and C. Jones, “Yoked surface codes”, (2023) arXiv:2312.04522
[2]
D. Poulin, “Optimal and efficient decoding of concatenated quantum block codes”, Physical Review A 74, (2006) arXiv:quant-ph/0606126 DOI
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Zoo Code ID: yoked_surface

Cite as:
“Yoked surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/yoked_surface
BibTeX:
@incollection{eczoo_yoked_surface, title={Yoked surface code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/yoked_surface} }
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Permanent link:
https://errorcorrectionzoo.org/c/yoked_surface

Cite as:

“Yoked surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/yoked_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/concatenated/yoked_surface.yml.