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

Cousin

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
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Zoo code information

Internal code ID: random_circuit

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Zoo Code ID: random_circuit

Cite as:
“Random-circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/random_circuit
BibTeX:
@incollection{eczoo_random_circuit, title={Random-circuit code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/random_circuit} }
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Permanent link:
https://errorcorrectionzoo.org/c/random_circuit

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.