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
- Victor V. Albert (2024-04-12) — most recent
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