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 fault-tolerant 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. Admits pseudo-thresholds of \(\approx 10^{-4}\) under depolarizing noise.

Encoding

Measurement-free fault-tolerant logical zero state preparation in nearest-neighbor qubit connectivity [2].Fault-tolerant logical zero and logical plus state preparation in all-to-all and 2D grid connectivity with flag qubits [3].

Transversal Gates

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

Decoding

Lookup table [1].

Fault Tolerance

Measurement-free fault-tolerant logical zero state preparation in nearest-neighbor qubit connectivity [2].Fault-tolerant logical zero and logical plus state preparation in all-to-all and 2D grid connectivity with flag qubits [3].

Realizations

Implemented at ETH Zurich by the Wallraff group [4] and on the Zuchongzhi 2.1 superconducting quantum processor [5]. Both experimental error rates are above the pseudo-threshold for this code relative to a single qubit; see Physics viewpoint for a summary [6]. Magic state have been created on the latter processor [7].

Notes

Subject of various numerical studies examining the system for noises and architectures specific to trapped ions [1,8,9] and superconducting circuits [1012]

Parents

Cousins

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]
H. Goto, Y. Ho, and T. Kanao, “Measurement-free fault-tolerant logical-zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array”, Physical Review Research 5, (2023) arXiv:2303.17211 DOI
[3]
R. Zen et al., “Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning”, (2024) arXiv:2402.17761
[4]
S. Krinner et al., “Realizing repeated quantum error correction in a distance-three surface code”, Nature 605, 669 (2022) arXiv:2112.03708 DOI
[5]
Y. Zhao et al., “Realization of an Error-Correcting Surface Code with Superconducting Qubits”, Physical Review Letters 129, (2022) arXiv:2112.13505 DOI
[6]
L. Frunzio and S. Singh, “Error-Correcting Surface Codes Get Experimental Vetting”, Physics 15, (2022) DOI
[7]
Y. Ye et al., “Logical Magic State Preparation with Fidelity Beyond the Distillation Threshold on a Superconducting Quantum Processor”, (2023) arXiv:2305.15972
[8]
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
[9]
D. M. Debroy et al., “Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors”, (2020) arXiv:1910.08495
[10]
R. Versluis et al., “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Physical Review Applied 8, (2017) arXiv:1612.08208 DOI
[11]
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
[12]
B. M. Varbanov et al., “Leakage detection for a transmon-based surface code”, npj Quantum Information 6, (2020) arXiv:2002.07119 DOI
[13]
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.), 2024. https://errorcorrectionzoo.org/c/surface-17
BibTeX:
@incollection{eczoo_surface-17, title={Surface-17 code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/surface-17} }
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“Surface-17 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/surface-17

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface-17.yml.