Random quantum code 

Description

Quantum code whose construction is non-deterministic in some way, i.e., codes that utilize an elements of randomness somewhere in their construction. Members of this class range from fully non-deterministic codes (e.g., random-circuit codes), to codes whose multi-step construction is deterministic with the exception of a single step (e.g., expander lifter-product codes).

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References

[1]
S. Totey et al., “The performance of random bosonic rotation codes”, (2023) arXiv:2311.16089
[2]
P. Faist et al., “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI
[3]
L. Kong and Z.-W. Liu, “Near-Optimal Covariant Quantum Error-Correcting Codes from Random Unitaries with Symmetries”, PRX Quantum 3, (2022) arXiv:2112.01498 DOI
[4]
L. Golowich and V. Guruswami, “Quantum Locally Recoverable Codes”, (2023) arXiv:2311.08653
[5]
A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist”, Physical Review A 54, 1098 (1996) arXiv:quant-ph/9512032 DOI
[6]
J. Haah, “Towers of generalized divisible quantum codes”, Physical Review A 97, (2018) arXiv:1709.08658 DOI
[7]
M. H. Freedman and M. B. Hastings, “Quantum Systems on Non-\(k\)-Hyperfinite Complexes: A Generalization of Classical Statistical Mechanics on Expander Graphs”, (2013) arXiv:1301.1363
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Zoo Code ID: quantum_random

Cite as:
“Random quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_random
BibTeX:
@incollection{eczoo_quantum_random, title={Random quantum code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_random} }
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Cite as:

“Random quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_random

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/quantum_random.yml.