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Modified logarithmic Sobolev inequalities for CSS codes

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Sebastian Stengele, Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, Antonio Pérez-Hernández, Cambyse Rouzé, Simone Warzel

Quantum Physics · Submitted 3 Oct 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2510.03090 (version 2)
Pith IDZ5QQ2CK7, Pith's permanent record of this paper and its review
Citation\'Angela Capel, Angelo Lucia, Antonio P\'erez-Hern\'andez, Cambyse Rouz\'e, David P\'erez-Garc\'ia, Li Gao, Sebastian Stengele, Simone Warzel. "Modified logarithmic Sobolev inequalities for CSS codes." arXiv:2510.03090 (2025). https://pith.science/paper/Z5QQ2CK7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,722 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.38 · compares with prior results 0.56 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the class of Davies quantum semigroups modelling thermalization for translation-invariant Calderbank-Shor-Steane (CSS) codes in D dimensions. background 0.64 0.40 0.03 asserted 0.66
s1 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. result 0.94 0.96 0.80 asserted 1.00
s2 This is accomplished by generalizing parts of the classical results on thermalization by Stroock, Zegarlinski, Martinelli, and Olivieri to the CSS quantum setting. method 0.98 0.74 0.06 asserted 1.00
s3 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. interpretation 0.94 0.88 0.52 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper
Original 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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References
How the literature uses it

1 arXiv paper cite this in 14 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 7 sentences without a confident label

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What it cites · 17 sentences without a confident label

Compares with 3 papers
  • In the particular case of the toric code in 2D, this implies that the previous work [ref] yielded a circuit depth of $𝒪(n^2 polylog n)$, and that of [ref] , a depth of $𝒪(n^4 polylog n)$, the latter with a linear dependence on $β$ and the former with an exponential dependence.

    Polynomial-Time Preparation of Low-Temperature Gibbs States for 2D Toric Code · Comparison to existing literature · 0.98

  • Additionally, alternative approaches based on duality of the Hamiltonians with classical models, provide a circuit complexity of $𝒪(n^3/2)$ [ref] for the $2$D toric code, and of $𝒪(n^2)$ [ref] for the defective toric code, both independently of $β$.

    Gibbs state preparation for commuting Hamiltonian: Mapping to classical Gibbs sampling · Comparison to existing literature · 0.95

  • Additionally, alternative approaches based on duality of the Hamiltonians with classical models, provide a circuit complexity of $𝒪(n^3/2)$ [ref] for the $2$D toric code, and of $𝒪(n^2)$ [ref] for the defective toric code, both independently of $β$.

    2508.00126 · Comparison to existing literature · 0.95

Cites as background 3 papers
  • The classical MCMC algorithm inspired many quantum algorithms for the preparation of quantum Gibbs states [ref] , starting with the seminal quantum Metropolis algorithm [ref] .

    2405.20322 · Comparison to existing literature · 0.91

  • The classical MCMC algorithm inspired many quantum algorithms for the preparation of quantum Gibbs states [ref] , starting with the seminal quantum Metropolis algorithm [ref] .

    Quantum Metropolis Sampling via Weak Measurement · Comparison to existing literature · 0.91

  • We use the symbols $$ and $$ in reminiscence of the equivalence of CSS codes to (co-)chain complexes, see e.g. [ref] .

    PhD thesis: Homological Quantum Codes Beyond the Toric Code · Families of CSS Hamiltonians · 0.88

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