Renormalization group and approximate error correction

Abstract

In renormalization group (RG) flow, the low energy states form a code subspace that is approximately protected against the local short-distance errors. We motivate this connection with an example of spin-blocking RG in classical spin models. We consider the continuous multi-scale renormalization ansatz (cMERA) for massive free fields as a concrete example of real-space RG in quantum field theory (QFT) and show that the low-energy coherent states are approximately protected from the errors caused by the high-energy localized coherent operators. In holographic RG flows, we study the phase transition in the entanglement wedge of a single region and argue that one needs to define the price and the distance of the code with respect to the reconstructable wedge.

References in corpus (8)

• Holographic c-theorems in arbitrary dimensions
• Causality & holographic entanglement entropy
• Seeing a c-theorem with holography
• Entanglement renormalization and topological order
• Exact entanglement renormalization for string-net models
• Quantum error correction on infinite-dimensional Hilbert spaces
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Magic entanglement renormalization for quantum fields

Cited by in corpus (6)

• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Exact Renormalization of Wave Functionals yields Continuous MERA
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• A Lindbladian for exact renormalization of density operators in QFT
• Quantum error correction realized by the renormalization group in scalar field theories