[2508.00126] Environment friendly and easy Gibbs state preparation of the 2D toric code through duality to classical Ising chains

View a PDF of the paper titled Environment friendly and easy Gibbs state preparation of the 2D toric code through duality to classical Ising chains, by Pablo P’aez-Velasco and three different authors

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Summary:We introduce the notion of polynomial-depth duality transformations, which relates two units of operator algebras by means of a conjugation by a poly-depth quantum circuit, and make use of this to assemble environment friendly Gibbs samplers for a wide range of attention-grabbing quantum Hamiltonians as they’re poly-depth twin to classical Hamiltonians. That is for instance the case for the 2D toric code, which is demonstrated to be poly-depth twin to 2 decoupled classical Ising spin chains for any system dimension, and we give proof that such dualities maintain for a large class of stabilizer Hamiltonians. Moreover, we prolong the above notion of duality to Lindbladians to be able to present that mixing instances and different portions such because the spectral hole or the modified logarithmic Sobolev inequality are preserved beneath duality.