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
- Haar-random code
- Local Haar-random circuit code
- Low-depth random Clifford-circuit code
- Monitored random-circuit code — Monitored random circuits are random circuits where projective measurements are interspersed throughout the circuit and measurement results are recorded.
Cousin
- Crystalline-circuit 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). DOI; quant-ph/9910081
- [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). DOI; 0810.1983
- [3]
- M. J. Gullans and D. A. Huse, “Dynamical Purification Phase Transition Induced by Quantum Measurements”, Physical Review X 10, (2020). DOI; 1905.05195
- [4]
- A. C. Potter and R. Vasseur, “Entanglement Dynamics in Hybrid Quantum Circuits”, Quantum Science and Technology 211 (2022). DOI; 2111.08018
- [5]
- Matthew P. A. Fisher et al., “Random Quantum Circuits”. 2207.14280
Page edit log
- Victor V. Albert (2021-11-30) — most recent
Zoo code information
Cite as:
“Random-circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/random_circuit