Rotated surface code[1][2][3][4]

Description

Variant of the surface code defined on a square lattice that has been rotated 45 degrees such that qubits are on vertices, and both \(X\)- and \(Z\)-type check operators occupy plaquettes in an alternating checkerboard pattern.

Fault Tolerance

A particular choice of CNOT gates during syndrome extraction is required to be fault-tolerant to syndrome qubit errors [4].

Parents

Child

Cousins

  • Heavy-hexagon code — A rotated surface code can be mapped onto a heavy square lattice, resulting in a code similar to the heavy-hexagon code [6].
  • XZZX surface code — XZZX code is obtained from the rotated surface code by applying Hadamard gates on a subset of qubits such that \(XXXX\) and \(ZZZZ\) generators are both mapped to \(XZXZ\).
  • \([[4,2,2]]\) CSS code — Various \([[4,1,2]]\) subcodes are small rotated planar codes [7][8][9][10].

Zoo code information

Internal code ID: rotated_surface

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: rotated_surface

Cite as:
“Rotated surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rotated_surface
BibTeX:
@incollection{eczoo_rotated_surface, title={Rotated surface code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rotated_surface} }
Permanent link:
https://errorcorrectionzoo.org/c/rotated_surface

References

[1]
X.-G. Wen, “Quantum Orders in an Exact Soluble Model”, Physical Review Letters 90, (2003). DOI; quant-ph/0205004
[2]
H. Bombin and M. A. Martin-Delgado, “Optimal resources for topological two-dimensional stabilizer codes: Comparative study”, Physical Review A 76, (2007). DOI; quant-ph/0703272
[3]
Jonas T. Anderson, “Homological Stabilizer Codes”. 1107.3502
[4]
Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise”, Physical Review A 90, (2014). DOI; 1404.3747
[5]
Nikolas P. Breuckmann, private communication, 2022
[6]
C. Chamberland et al., “Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits”, Physical Review X 10, (2020). DOI; 1907.09528
[7]
A. Erhard et al., “Entangling logical qubits with lattice surgery”, Nature 589, 220 (2021). DOI; 2006.03071
[8]
C. K. Andersen et al., “Repeated quantum error detection in a surface code”, Nature Physics 16, 875 (2020). DOI; 1912.09410
[9]
Zijun Chen et al., “Exponential suppression of bit or phase flip errors with repetitive error correction”. 2102.06132
[10]
J. F. Marques et al., “Logical-qubit operations in an error-detecting surface code”, Nature Physics 18, 80 (2021). DOI; 2102.13071

Cite as:

“Rotated surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rotated_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/topological/surface/rotated_surface.yml.