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Abstract
We demonstrate that quantum error correction is realized by the renormalization group in scalar field theories. We construct q-level states by using coherent states in the IR region. By acting on them the inverse of the unitary operator U that describes the renormalization group flow of the ground state, we encode them into states in the UV region. We find the situations in which the Knill–Laflamme condition is satisfied for operators that create coherent states. We verify this to the first order in the perturbation theory. This result suggests a general relationship between the renormalization group and quantum error correction and should give insights into understanding the role played by them in the gauge/gravity correspondence.
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Details
1 Department of Physics, Kyoto University , Sakyo-ku, Kyoto 606-8502 , Japan
2 Graduate School of Science and Technology, Shizuoka University , 836 Ohya, Suruga-ku, Shizuoka 422-8529 , Japan
3 Institute for Mathematical Informatics, Meiji Gakuin University , 1518 Kamikuratacho, Totsuka-ku, Yokohama 244-8539 , Japan