[Jump to code hierarchy]

Log-depth geometrically local Clifford-circuit code[1,2]

Description

A random \([[n,k]]\) stabilizer code whose encoder is a random Clifford circuit of depth of order \(O(\log n)\) on a 1D Euclidean geometry.

Rate

Log-depth Clifford circuits on a 1D geometry yield approximate codes whose encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors [2].

Encoding

Random \(\log\)-depth Clifford circuit on a 1D Euclidean geometry.

Decoding

Minimum-weight decoding via using tropical tensor networks [1].

Fault Tolerance

Fault-tolerant state preparation [1].

Primary Hierarchy

Parents
Log-depth Clifford circuits on a 1D geometry yield approximate codes whose encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors [2].
Log-depth Clifford circuits on a 1D geometry yield approximate codes whose encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors [2].
Log-depth geometrically local Clifford-circuit code

References

[1]
J. Nelson, G. Bentsen, S. T. Flammia, and M. J. Gullans, “Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes”, (2023) arXiv:2311.17985
[2]
G. Liu, Z. Du, Z.-W. Liu, and X. Ma, “Approximate Quantum Error Correction with 1D Log-Depth Circuits”, (2025) arXiv:2503.17759
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: approximate_log_depth

Cite as:
“Log-depth geometrically local Clifford-circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/approximate_log_depth
BibTeX:
@incollection{eczoo_approximate_log_depth, title={Log-depth geometrically local Clifford-circuit code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/approximate_log_depth} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/approximate_log_depth

Cite as:

“Log-depth geometrically local Clifford-circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/approximate_log_depth

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/dynamic/random/approximate_log_depth.yml.