Approximate quantum error correcting codes from conformal field theory

• URL: http://arxiv.org/abs/2406.09555v3
• Date: Sat, 09 Nov 2024 13:29:38 GMT
• Title: Approximate quantum error correcting codes from conformal field theory
• Authors: Shengqi Sang, Timothy H. Hsieh, Yijian Zou,
• Abstract summary: We consider generic 1+1D CFT codes under extensive local dephasing channels. We show that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.
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• Abstract: The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing channels and analyze their error correctability in the thermodynamic limit. We show that (i) there is a finite decoding threshold if and only if the minimal nonzero scaling dimension in the fusion algebra generated by the jump operator of the channel is larger than $1/2$ and (ii) the number of protected logical qubits $k \geq \Omega( \log \log n)$, where $n$ is the number of physical qubits. As an application, we show that the one-dimensional quantum critical Ising model has a finite threshold for certain types of dephasing noise. Our general results also imply that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.

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