Description
Error-detecting four-qubit subsystem stabilizer code encoding one logical qubit and one gauge qubit.
The \([[4,1,1,2]]\) code can be obtained by picking one of the logical qubits of the \([[4,2,2]]\) four-qubit code to be a gauge qubit; e.g., see Ref. [3]. One particular gauge configuration has gauge group \(\mathsf{G}=\langle i,XXII,IIXX,ZIZI,IZIZ \rangle\).
Parent
- Bacon-Shor code — The four-qubit subsystem code is the shortest error-detecting Bacon-Shor code.
Cousins
- \([[4,2,2]]\) Four-qubit code — The \([[4,1,1,2]]\) code can be obtained by picking one of the logical qubits of the \([[4,2,2]]\) four-qubit code to be a gauge qubit; e.g., see Ref. [3]. One particular gauge configuration has gauge operators \(\{XXII,IIXX,ZIZI,IZIZ\}\).
- Holographic hybrid code — The holographic hybrid code is constructed out of alternating isometries of the five-qubit and \([[4,1,1,2]]\) Bacon-Shor codes.
- Raussendorf-Bravyi-Harrington (RBH) cluster-state code — Concatenation of the RBH code with small codes such as the \([[2,1,1]]\) repetition code, \([[4,1,1,2]]\) subsystem code, or Steane code can improve thresholds [4].
References
- [1]
- P. W. Shor, “Scheme for reducing decoherence in quantum computer memory”, Physical Review A 52, R2493 (1995) DOI
- [2]
- D. Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories”, Physical Review A 73, (2006) arXiv:quant-ph/0506023 DOI
- [3]
- V. V. Albert, Boulder School 2023 Lecture notes
- [4]
- Z. Li, I. Kim, and P. Hayden, “Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction”, Quantum 7, 1089 (2023) arXiv:2209.09390 DOI
Page edit log
- Victor V. Albert (2024-07-01) — most recent
Cite as:
“\([[4,1,1,2]]\) Four-qubit subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bacon_shor_4