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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 2: Quantum Information and Gravity
MP 2.3: Talk
Monday, March 18, 2024, 10:40–11:00, HL 102
Correlations of the Toric code at finite temperature — •Sebastian Stengele1, Cambyse Rouzé2, Angela Capel3, and Simone Warzel1 — 1Department of Mathematics, Technical University of Munich, 85748 Garching, Deutschland — 2Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, 91120 Palaiseau, France — 3AB Mathematische Physik, Universität Tübingen, 72076 Tübingen, Deutschland
The toric code is a key example of a topological quantum error-correcting code and a potential candidate for a scalable quantum memory. We explore the decay of correlations of distant observables at finite temperatures. Leveraging techniques from classical statistical mechanics, we bound the correlations of the D≥2 dimensional toric code by truncated correlation functions of certain Ising models with many-body interactions. Furthermore, we show that these correlations decay exponentially at very high temperatures.
Keywords: Toric Code; Decay of correlations; Ising model