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Qubit c-q code

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

BP with quantum messages (BPQM) decoder [2–6].

Realizations

Quantum enhancement was demonstrated using a polarization-based non-error-correcting c-q encodings [7].

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.

Member of code lists

Primary Hierarchy

Classical-quantum Domain
Binary c-q Kingdom
Parents
Classical-quantum (c-q) code
Qubit c-q code
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

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
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Zoo Code ID: qubit_classical_into_quantum

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
BibTeX:
@incollection{eczoo_qubit_classical_into_quantum, title={Qubit c-q code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qubit_classical_into_quantum} }
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Permanent link:
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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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical_into_quantum/qubits/qubit_classical_into_quantum.yml.