Surface-17 code[1] 


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 fault-tolerant error correction on a surface code with parallel syndrome extraction.


Independent correction of single-qubit \(X\) and \(Z\) errors. Correction for some two-qubit \(X\) and \(Z\) errors. Admits pseudo-thresholds of \(\sim 10^{-4}\) under depolarizing noise.

Transversal Gates

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


Lookup table [1].


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 pseudo-threshold 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].


Subject of various numerical studies examining the system for noises and architectures specific to trapped ions [1,6,7] and superconducting circuits [810]




Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise”, Physical Review A 90, (2014) arXiv:1404.3747 DOI
S. Krinner et al., “Realizing repeated quantum error correction in a distance-three surface code”, Nature 605, 669 (2022) arXiv:2112.03708 DOI
Y. Zhao et al., “Realization of an Error-Correcting Surface Code with Superconducting Qubits”, Physical Review Letters 129, (2022) arXiv:2112.13505 DOI
L. Frunzio and S. Singh, “Error-Correcting Surface Codes Get Experimental Vetting”, Physics 15, (2022) DOI
Y. Ye et al., “Logical Magic State Preparation with Fidelity Beyond the Distillation Threshold on a Superconducting Quantum Processor”, (2023) arXiv:2305.15972
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
D. M. Debroy et al., “Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors”, (2020) arXiv:1910.08495
R. Versluis et al., “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Physical Review Applied 8, (2017) arXiv:1612.08208 DOI
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
B. M. Varbanov et al., “Leakage detection for a transmon-based surface code”, npj Quantum Information 6, (2020) arXiv:2002.07119 DOI
J. Conrad et al., “The small stellated dodecahedron code and friends”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, 20170323 (2018) arXiv:1712.07666 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.
@incollection{eczoo_surface-17, title={Surface-17 code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Cite as:

“Surface-17 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.