Random-circuit code

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

See Refs. [4][5] for reviews on random-circuit codes.

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

Cite as:

“Random-circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/random_circuit

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/dynamic_gen/random_circuit.yml.