Description
Approximate code whose codewords lie in the low-energy subspace of a conformal field theory, e.g., the quantum Ising model at its critical point [1,3]. Its encoding is argued to perform source coding (i.e., compression) as well as channel coding (i.e., error correction) [1].Protection
Code performance is quantified by a lower bound on the entanglement fidelity in terms of the conditional mutual information [1; Eq. (9)]; see also [4; Appx. A]. Certain CFT codes have indefinite codespace complexity, and their protection depends on the minimum scaling dimension of the underlying CFT [2]. The coherent information of a combined noise and recovery channel can be perturbatively expanded [3].Code Capacity Threshold
Threshold under dephasing depends on the structure of the conformal field theory, with the 1D critical Ising model admitting a finite threshold against certain dephasing noise [3].Cousin
- Qubit CSS code— There is a holographic relation between qubit CSS codes describing CFTs and qubit stabilizer codes describing path integrals over certain topologies [5].
Primary Hierarchy
Parents
CFT codewords lie in the low-energy subspace of a conformal field theory (CFT), e.g., the quantum Ising model at its critical point.
CFT codewords lie in the low-energy subspace of a conformal field theory (CFT), e.g., the quantum Ising model at its critical point.
Conformal-field theory (CFT) code
References
- [1]
- F. Pastawski, J. Eisert, and H. Wilming, “Towards Holography via Quantum Source-Channel Codes”, Physical Review Letters 119, (2017) arXiv:1611.07528 DOI
- [2]
- J. Yi, W. Ye, D. Gottesman, and Z.-W. Liu, “Complexity and order in approximate quantum error-correcting codes”, Nature Physics (2024) arXiv:2310.04710 DOI
- [3]
- S. Sang, T. H. Hsieh, and Y. Zou, “Approximate quantum error correcting codes from conformal field theory”, (2024) arXiv:2406.09555
- [4]
- K. Noh, V. V. Albert, and L. Jiang, “Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes”, IEEE Transactions on Information Theory 65, 2563 (2019) arXiv:1801.07271 DOI
- [5]
- A. Dymarsky, J. Henriksson, and B. McPeak, “Holographic duality from Howe duality: Chern-Simons gravity as an ensemble of code CFTs”, (2025) arXiv:2504.08724
Page edit log
- Victor V. Albert (2024-07-02) — most recent
Cite as:
“Conformal-field theory (CFT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cft
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/holographic/cft.yml.