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arXiv · 2406.09555

Approximate quantum error correcting codes from conformal field theory

Shengqi Sang·Timothy H. Hsieh·Yijian Zou
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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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Shengqi Sang, Timothy H. Hsieh, Yijian Zou. 2024-06-13. Approximate quantum error correcting codes from conformal field theory. https://arxiv.org/abs/2406.09555

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