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 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.

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 pseudothreshold for this code relative to a single qubit.


Subject of various numerical studies examining the system for noises and architectures specific to trapped ions [1][4][5] and superconducting circuits [6][7][8]


Zoo code information

Internal code ID: surface-17

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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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Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise”, Physical Review A 90, (2014). DOI; 1404.3747
Sebastian Krinner et al., “Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code”. 2112.03708
Youwei Zhao et al., “Realization of an Error-Correcting Surface Code with Superconducting Qubits”. 2112.13505
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). DOI; 1710.01378
Dripto M. Debroy et al., “Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors”. 1910.08495
R. Versluis et al., “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Physical Review Applied 8, (2017). DOI; 1612.08208
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). DOI; 1703.04136
B. M. Varbanov et al., “Leakage detection for a transmon-based surface code”, npj Quantum Information 6, (2020). DOI; 2002.07119

Cite as:

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