Modified logarithmic Sobolev inequalities for CSS codes

2025/10/03 by Sebastian Stengele, Stengele, Sebastian, Ángela Capel +13
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Quantum Information and Cryptography

paper · pdf · doi:10.48550/arxiv.2510.03090

Abstract

We consider the class of Davies quantum semigroups modelling thermalization for translation-invariant Calderbank-Shor-Steane (CSS) codes in D dimensions. We prove that conditions of Dobrushin-Shlosman-type on the quantum Gibbs state imply a modified logarithmic Sobolev inequality with a constant that is uniform in the system's size. This is accomplished by generalizing parts of the classical results on thermalization by Stroock, Zegarlinski, Martinelli, and Olivieri to the CSS quantum setting. The results in particular imply the rapid thermalization at any positive temperature of the toric code in 2D and the star part of the toric code in 3D, implying a rapid loss of stored quantum information for these models.

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Cited by

• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains

Related

• Coherent information for CSS codes under decoherence
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions
• Thermalization time bounds for Pauli stabilizer Hamiltonians
• Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
• Ungauging quantum error-correcting codes