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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).

Protection

Certain random codes have nontrivial codespace complexity [1].

Cousins

References

[1]
J. Yi, W. Ye, D. Gottesman, and Z.-W. Liu, “Complexity and order in approximate quantum error-correcting codes”, Nature Physics (2024) arXiv:2310.04710 DOI
[2]
S. Totey, A. Kyle, S. Liu, P. J. Barge, N. Lordi, and J. Combes, “The performance of random bosonic rotation codes”, (2023) arXiv:2311.16089
[3]
L. Kong and Z.-W. Liu, “Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes”, (2021) arXiv:2102.11835
[4]
P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI
[5]
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
[6]
L. Golowich and V. Guruswami, “Quantum Locally Recoverable Codes”, (2023) arXiv:2311.08653
Page edit log

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.