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].
Parent
Child
Cousins
- Random code
- Bosonic rotation code — Random bosonic rotation codes can outperform cat and binomial codes when loss rate is large relative to dephasing rate [2].
- 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 [3] and \(U(d)\)-covariant [4,5] 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 [6; Prop. 5].
References
- [1]
- J. Yi et al., “Complexity and order in approximate quantum error-correcting codes”, (2024) arXiv:2310.04710
- [2]
- S. Totey et al., “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 et al., “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
- 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