Surface-17 code[1] 

Description

A \([[9,1,3]]\) rotated surface code named for the sum of its 9 data qubits and 8 syndrome qubits. It uses the smallest number of qubits to perform error correction on a surface code with parallel syndrome extraction.

Protection

Independent correction of single-qubit \(X\) and \(Z\) errors. Correction for some two-qubit \(X\) and \(Z\) errors.

Transversal Gates

Pauli gates, CNOT gate, and \(H\) gate (with relabeling).

Decoding

Lookup table [1].

Realizations

Implemented at ETH Zurich by the Wallraff group [2] and on the Zuchongzhi 2.1 superconducting quantum processor [3]. Both experimental error rates are above the pseudothreshold for this code relative to a single qubit; see Physics viewpoint for a summary [4]. Magic state have been created on the latter processor [5].

Notes

Subject of various numerical studies examining the system for noises and architectures specific to trapped ions [1,6,7] and superconducting circuits [8–10]

Parent

References

[1]
Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise”, Physical Review A 90, (2014) arXiv:1404.3747 DOI
[2]
S. Krinner et al., “Realizing repeated quantum error correction in a distance-three surface code”, Nature 605, 669 (2022) arXiv:2112.03708 DOI
[3]
Y. Zhao et al., “Realization of an Error-Correcting Surface Code with Superconducting Qubits”, Physical Review Letters 129, (2022) arXiv:2112.13505 DOI
[4]
L. Frunzio and S. Singh, “Error-Correcting Surface Codes Get Experimental Vetting”, Physics 15, (2022) DOI
[5]
Y. Ye et al., “Logical Magic State Preparation with Fidelity Beyond the Distillation Threshold on a Superconducting Quantum Processor”, (2023) arXiv:2305.15972
[6]
C. J. Trout et al., “Simulating the performance of a distance-3 surface code in a linear ion trap”, New Journal of Physics 20, 043038 (2018) arXiv:1710.01378 DOI
[7]
D. M. Debroy et al., “Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors”, (2020) arXiv:1910.08495
[8]
R. Versluis et al., “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Physical Review Applied 8, (2017) arXiv:1612.08208 DOI
[9]
T. E. O’Brien, B. Tarasinski, and L. DiCarlo, “Density-matrix simulation of small surface codes under current and projected experimental noise”, npj Quantum Information 3, (2017) arXiv:1703.04136 DOI
[10]
B. M. Varbanov et al., “Leakage detection for a transmon-based surface code”, npj Quantum Information 6, (2020) arXiv:2002.07119 DOI
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Zoo Code ID: surface-17

Cite as:
“Surface-17 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/surface-17
BibTeX:
@incollection{eczoo_surface-17,
  title={Surface-17 code},
  booktitle={The Error Correction Zoo},
  year={2022},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/surface-17}
}
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Permanent link:
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Cite as:

“Surface-17 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/surface-17

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface-17.yml.