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).
Parent
Child
Cousins
- Random code
- Covariant code — Random \(U(d)\)-covariant almost exactly error-correcting codes exist [1][2].
- Calderbank-Shor-Steane (CSS) stabilizer code — Random CSS codes asymptotically achieve linear distance with high probability, achieving the quantum Gilbert-Varshamov bound [3].
- Fiber-bundle code
- Homological product code — Random homological codes are asymptotically good with high probability [4; Thm. 1].
- Clifford-deformed surface code (CDSC) — Many useful CDSCs are constructed using random Clifford circuits.
References
- [1]
- P. Faist et al., “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI
- [2]
- 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
- [3]
- A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist”, Physical Review A 54, 1098 (1996) arXiv:quant-ph/9512032 DOI
- [4]
- 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
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