Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature

Helmuth, Tyler; Mann, Ryan L.

doi:10.48550/arxiv.2201.06533

Cited by 1 publication

(2 citation statements)

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“…Other results on particular classes of models recently studied are e.g. those of [100] a class of dense Hamiltionians was shown to have an efficient algorithm, while in [29] a class of quantum models close to classical ones was shown to have a convergent cluster expansion even at low temperatures. There also exists quantum algorithms for approximating general partition functions [100,105] in the sense of Eq.…”

Section: B Hardness Of Approximating Partition Functionsmentioning

confidence: 99%

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Quantum many-body systems in thermal equilibrium

Alhambra¹

2022

Preprint

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The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics, high energy physics, quantum chemistry and quantum computing, among others. We give a pedagogical overview of some of the most important universal features about the physics and complexity of these states, which have the locality of the Hamiltonian at its core. We focus on mathematically rigorous statements, many of them inspired by ideas and tools from quantum information theory. These include bounds on their correlations, the form of the subsystems, various statistical properties, and the performance of classical and quantum algorithms. We also include a summary of a few of the most important technical tools, as well as some self-contained proofs.Parts of these notes were the basis for a lecture series within the "Quantum Thermo-

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Section: B Hardness Of Approximating Partition Functionsmentioning

confidence: 99%

“…Let us note, however, that there are specific models in the literature for which the convergence can be guaranteed for larger ranges of temperatures (see e.g. [29] and references therein). See Sec.…”

Section: A Connected Cluster Expansionmentioning

confidence: 99%

Quantum many-body systems in thermal equilibrium

Alhambra¹

2022

Preprint

View full text Add to dashboard Cite

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Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature

Cited by 1 publication

References 20 publications

Quantum many-body systems in thermal equilibrium

Quantum many-body systems in thermal equilibrium

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