Description
A qubit stabilizer code for which two binary linear codes are used to directly construct encoding and decoding circuits against \(X\)- and \(Z\)-type errors, respectively, via ZX calculus [4,5]. CPC codes can be obtained from numerical search [2].
Parent
- Qubit stabilizer code — CPC codes are a type of stabilizer code. A teleported version of the CPC construction can reduce noise in Clifford circuits with Pauli measurements with at most a three-fold overhead in the number of qubits and gates [6]. There is a simple formula for the probability that a Clifford circuit contains a logical error [3].
Child
- Qubit CSS code — CSS codes are a subset of CPC codes [1], with the latter not requiring the two classical codes to be related.
Cousins
- Linear binary code — The CPC Construction uses two binary linear codes.
- \([2^r-1,2^r-r-1,3]\) Hamming code — Tripartite CPC codes are constructed from Hamming codes via the CPC construction [1; Thm. 4].
- \([[4,2,2]]\) Four-qubit code — CPC gadgets for the \([[4,2,2]]\) code have been implemented on the IBM 5Q superconducting device [2].
References
- [1]
- N. Chancellor et al., “Graphical structures for design and verification of quantum error correction”, Quantum Science and Technology 8, 045028 (2023) arXiv:1611.08012 DOI
- [2]
- J. Roffe et al., “Protecting quantum memories using coherent parity check codes”, Quantum Science and Technology 3, 035010 (2018) arXiv:1709.01866 DOI
- [3]
- D. M. Debroy and K. R. Brown, “Extended flag gadgets for low-overhead circuit verification”, Physical Review A 102, (2020) arXiv:2009.07752 DOI
- [4]
- B. Coecke and R. Duncan, “Interacting Quantum Observables”, Automata, Languages and Programming 298 DOI
- [5]
- B. Coecke and R. Duncan, “Interacting quantum observables: categorical algebra and diagrammatics”, New Journal of Physics 13, 043016 (2011) arXiv:0906.4725 DOI
- [6]
- N. Delfosse and E. Tham, “Low-cost noise reduction for Clifford circuits”, (2024) arXiv:2407.06583
Page edit log
- Victor V. Albert (2023-11-14) — most recent
Cite as:
“Coherent-parity-check (CPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/cpc
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/cpc.yml.