Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909715452133376 |
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| author | Páez-Velasco, Pablo Schilling, Niclas Scalet, Samuel O. Verstraete, Frank Capel, Ángela |
| author_facet | Páez-Velasco, Pablo Schilling, Niclas Scalet, Samuel O. Verstraete, Frank Capel, Ángela |
| contents | We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety of interesting quantum Hamiltonians as they are poly-depth dual to classical Hamiltonians. This is for example the case for the 2D toric code, which is demonstrated to be poly-depth dual to two decoupled classical Ising spin chains for any system size, and we give evidence that such dualities hold for a wide class of stabilizer Hamiltonians. Additionally, we extend the above notion of duality to Lindbladians in order to show that mixing times and other quantities such as the spectral gap or the modified logarithmic Sobolev inequality are preserved under duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains Páez-Velasco, Pablo Schilling, Niclas Scalet, Samuel O. Verstraete, Frank Capel, Ángela Quantum Physics Statistical Mechanics Mathematical Physics We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety of interesting quantum Hamiltonians as they are poly-depth dual to classical Hamiltonians. This is for example the case for the 2D toric code, which is demonstrated to be poly-depth dual to two decoupled classical Ising spin chains for any system size, and we give evidence that such dualities hold for a wide class of stabilizer Hamiltonians. Additionally, we extend the above notion of duality to Lindbladians in order to show that mixing times and other quantities such as the spectral gap or the modified logarithmic Sobolev inequality are preserved under duality. |
| title | Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2508.00126 |