Description
A qubit code which stores both quantum and classical information. Usually denoted as \(((n,K:M))\) or \(((n,K:M,d))\), where \(K\) is the dimension of the underlying quantum code, where \(M\) is the size of the classical code, and where \(d\) is the distance.
Protection
Any qubit code can be converted into a hybrid qubit code by using some its qubits to store only classical information [1]. An \(((n,K:M))\) hybrid qubit code can detect more errors than an \(((n,KM))\) qubit code [3]. A hybrid Hamming bound has been constructed [4].
Quantum weight enumerators, quantum MacWilliams identities, and linear programming bounds have been extended to hybrid qubit codes [2,3,5].
Parents
- Operator-algebra (OA) qubit code — An OA qubit code which has no which has no gauge structure (e.g., gauge qubits) but has a block structure that corresponds to a classical code is a hybrid qubit code.
- Hybrid QECC
Child
- Hybrid stabilizer code — An \([[n,k:c,d]]\) hybrid stabilizer code is an \(((n,2^k:2^c,d))\) hybrid qubit code.
Cousins
- Qubit code — A hybrid qubit code storing no classical information reduces to a qubit code. Conversely, any qubit code can be converted into a hybrid qubit code by using some its qubits to store only classical information [1].
- Qubit c-q code — A hybrid qubit code storing no quantum information reduces to a qubit c-q code.
References
- [1]
- I. Kremsky, M.-H. Hsieh, and T. A. Brun, “Classical enhancement of quantum-error-correcting codes”, Physical Review A 78, (2008) arXiv:0802.2414 DOI
- [2]
- M. Grassl, S. Lu, and B. Zeng, “Codes for simultaneous transmission of quantum and classical information”, 2017 IEEE International Symposium on Information Theory (ISIT) (2017) arXiv:1701.06963 DOI
- [3]
- A. Nemec and A. Klappenecker, “Hybrid Codes”, 2018 IEEE International Symposium on Information Theory (ISIT) (2018) arXiv:1901.02913 DOI
- [4]
- S. Majidy, “A Unification of the Coding Theory and OAQEC Perspectives on Hybrid Codes”, International Journal of Theoretical Physics 62, (2023) arXiv:1806.03702 DOI
- [5]
- A. Nemec and A. Klappenecker, “Infinite Families of Quantum-Classical Hybrid Codes”, (2020) arXiv:1911.12260
Page edit log
- Victor V. Albert (2024-07-04) — most recent
Cite as:
“Hybrid qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hybrid_qubits_into_qubits