Description
Quantum code whose construction is non-deterministic in some way, i.e., codes that utilize an element 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 lifted-product codes).Rate
Haar random codes achieve the quantum Hamming bound [2].Cousins
- Random code— Random quantum codes are quantum analogues of random classical codes.
- Perfect quantum code— Haar random codes achieve the quantum Hamming bound [2].
- Bosonic rotation code— Random bosonic rotation codes can outperform cat and binomial codes when loss rate is large relative to dephasing rate [3].
- NTRU-GKP code— Several NTRU lattices come from randomized constructions, yielding constant-rate GKP code families whose largest decodable displacement length scales as \(O(\sqrt{n})\) with high probability.
- Covariant block quantum code— Random \(U(1)\)-covariant [4] and \(U(d)\)-covariant [5,6] approximate QECCs exist.
- Quantum locally recoverable code (QLRC)— Random QLRCs with qudit dimension \(q = 2^{O(r)}\) achieve a relative distance that is order \(O(1/r)\) below the Singleton-like QLRC bound [7; Prop. 5].
Primary Hierarchy
Parents
Random codes typically correct errors on average.
Random quantum code
Children
References
- [1]
- J. Yi, W. Ye, D. Gottesman, and Z.-W. Liu, “Complexity and order in approximate quantum error-correcting codes”, Nature Physics 20, 1798 (2024) arXiv:2310.04710 DOI
- [2]
- F. Ma, X. Tan, and J. Wright, “Haar random codes attain the quantum Hamming bound, approximately”, (2025) arXiv:2510.07158
- [3]
- 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
- [4]
- L. Kong and Z.-W. Liu, “Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes”, (2021) arXiv:2102.11835
- [5]
- 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
- [6]
- 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
- [7]
- L. Golowich and V. Guruswami, “Quantum Locally Recoverable Codes”, (2023) arXiv:2311.08653
Page edit log
- Victor V. Albert (2022-02-28) — most recent
Cite as:
“Random quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_random