Quantum Error Correction Realized by the Renormalization Group in Scalar Field Theories

• Published in: Progress of theoretical and experimental physics Vol. 2024; no. 8
• Main Authors: Kuwahara, Takaaki, Nasu, Ryota, Tanaka, Gota, Tsuchiya, Asato
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.08.2024
• Subjects: Error correction & detection; Gravity
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptae102

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.