Root code for the Binary c-q Kingdom
Description
Qubit code designed for transmission of classical information in the form of bits through non-classical channels.
Protection
Performance of a linear binary code over a channel is dual to the performance of its dual over a particular dual channel [1].
Decoding
Realizations
Quantum enhancement was demonstrated using a polarization-based non-error-correcting c-q encodings [7].
Parent
Children
- Lechner-Hauke-Zoller (LHZ) code — The LHZ code is an LDPC c-q code designed to convert the long-range interactions of a quantum annealer into local constraints.
- Polar c-q code
Cousins
- Binary code — Any binary code can be embedded into a qubit Hilbert space, and thus passed through a qubit channel, by associating length-\(n\) bitstrings with basis vectors in a Hilbert space over \(\mathbb{Z}_2^n\). For example, a bit of information can be embedded into a two-dimensional vector space by associating the two bit values with two basis vectors for the space.
- Hybrid qubit code — A hybrid qubit code storing no quantum information reduces to a qubit c-q code.
References
- [1]
- J. M. Renes, “Duality of Channels and Codes”, IEEE Transactions on Information Theory 64, 577 (2018) arXiv:1701.05583 DOI
- [2]
- J. M. Renes, “Belief propagation decoding of quantum channels by passing quantum messages”, New Journal of Physics 19, 072001 (2017) arXiv:1607.04833 DOI
- [3]
- C. Piveteau and J. M. Renes, “Quantum message-passing algorithm for optimal and efficient decoding”, Quantum 6, 784 (2022) arXiv:2109.08170 DOI
- [4]
- S. Brandsen, A. Mandal, and H. D. Pfister, “Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels”, (2022) arXiv:2207.04984
- [5]
- N. Rengaswamy, K. P. Seshadreesan, S. Guha, and H. D. Pfister, “Belief propagation with quantum messages for quantum-enhanced classical communications”, npj Quantum Information 7, (2021) arXiv:2003.04356 DOI
- [6]
- H. D. Pfister, C. Piveteau, J. M. Renes, and N. Rengaswamy, “Belief Propagation for Classical and Quantum Systems: Overview and Recent Results”, IEEE BITS the Information Theory Magazine 2, 20 (2022) DOI
- [7]
- R. J. Chapman, A. Karim, Z. Huang, S. T. Flammia, M. Tomamichel, and A. Peruzzo, “Beating the classical limits of information transmission using a quantum decoder”, Physical Review A 97, (2018) arXiv:1704.07036 DOI
Page edit log
- Victor V. Albert (2022-12-04) — most recent
Cite as:
“Qubit c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/qubit_classical_into_quantum