Random-circuit code[1]
Description
Code whose encoding is naturally constructed by randomly sampling from a large set of (not necessarily unitary) quantum circuits.
Protection
A useful proxy and upper bound to the code distance \(d\) is the contiguous code distance: the contiguous length (with periodic boundary conditions) of the shortest logical operator [2,3].
Notes
Parents
Children
- Monitored random-circuit code — Monitored random circuits are random circuits where projective measurements are interspersed throughout the circuit and measurement results are recorded.
- Random stabilizer code
- Haar-random qubit code
- Local Haar-random circuit qubit code
Cousin
- Crystalline-circuit qubit code — Crystalline-circuit codes can be thought of as random-circuit codes with symmetries.
References
- [1]
- D. Aharonov, “Quantum to classical phase transition in noisy quantum computers”, Physical Review A 62, (2000) arXiv:quant-ph/9910081 DOI
- [2]
- S. Bravyi and B. Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes”, New Journal of Physics 11, 043029 (2009) arXiv:0810.1983 DOI
- [3]
- M. J. Gullans and D. A. Huse, “Dynamical Purification Phase Transition Induced by Quantum Measurements”, Physical Review X 10, (2020) arXiv:1905.05195 DOI
- [4]
- A. C. Potter and R. Vasseur, “Entanglement Dynamics in Hybrid Quantum Circuits”, Quantum Science and Technology 211 (2022) arXiv:2111.08018 DOI
- [5]
- M. P. A. Fisher, V. Khemani, A. Nahum, and S. Vijay, “Random Quantum Circuits”, Annual Review of Condensed Matter Physics 14, 335 (2023) arXiv:2207.14280 DOI
Page edit log
- Victor V. Albert (2021-11-30) — most recent
Cite as:
“Random-circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/random_circuit