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Log-depth Clifford-circuit code[1]

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 [1].

Encoding

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

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Parents
Qubit stabilizer code
Random stabilizer codeDynamically generated Stabilizer Hamiltonian-based QECC AQECC Quantum
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 [1].
Lattice stabilizer codeQLDPC Stabilizer Hamiltonian-based QECC Quantum
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 [1].
Log-depth Clifford-circuit code

References

[1]
G. Liu, Z. Du, Z.-W. Liu, and X. Ma, “Approximate Quantum Error Correction with 1D Log-Depth Circuits”, (2025) arXiv:2503.17759
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Zoo Code ID: approximate_log_depth

Cite as:
“Log-depth 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 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} }
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Permanent link:
https://errorcorrectionzoo.org/c/approximate_log_depth

Cite as:

“Log-depth 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.