Qubit c-q code

Description

Qubit code designed for transmission of classical information in the form of bits through non-classical channels.

Performance of a linear binary code over a channel is dual to the performance of its dual over a particular dual channel [1].

BP with quantum messages (BPQM) decoder [2–4].

Quantum enhancement was demonstrated using a polarization-based non-error-correcting c-q encodings [5].

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

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.

[1]: J. M. Renes, “Duality of Channels and Codes”, IEEE Transactions on Information Theory 64, 577 (2018) arXiv:1701.05583 DOI
[2]: S. Brandsen, A. Mandal, and H. D. Pfister, “Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels”, (2022) arXiv:2207.04984
[3]: N. Rengaswamy et al., “Belief propagation with quantum messages for quantum-enhanced classical communications”, npj Quantum Information 7, (2021) arXiv:2003.04356 DOI
[4]: H. D. Pfister et al., “Belief Propagation for Classical and Quantum Systems: Overview and Recent Results”, IEEE BITS the Information Theory Magazine 2, 20 (2022) DOI
[5]: R. J. Chapman et al., “Beating the classical limits of information transmission using a quantum decoder”, Physical Review A 97, (2018) arXiv:1704.07036 DOI

Page edit log

“Qubit c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/qubit_classical_into_quantum