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Condensed Matter > Statistical Mechanics

arXiv:2308.05660 (cond-mat)
[Submitted on 10 Aug 2023]

Title:Thermodynamic Linear Algebra

Authors:Maxwell Aifer, Kaelan Donatella, Max Hunter Gordon, Thomas
Ahle, Daniel Simpson, Gavin E. Crooks, Patrick J. Coles
Download a PDF of the paper titled Thermodynamic Linear Algebra, by
Maxwell Aifer and 6 other authors
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    Abstract: Linear algebraic primitives are at the core of many
    modern algorithms in engineering, science, and machine learning.
    Hence, accelerating these primitives with novel computing
    hardware would have tremendous economic impact. Quantum computing
    has been proposed for this purpose, although the resource
    requirements are far beyond current technological capabilities,
    so this approach remains long-term in timescale. Here we consider
    an alternative physics-based computing paradigm based on
    classical thermodynamics, to provide a near-term approach to
    accelerating linear algebra.
    At first sight, thermodynamics and linear algebra seem to be
    unrelated fields. In this work, we connect solving linear algebra
    problems to sampling from the thermodynamic equilibrium
    distribution of a system of coupled harmonic oscillators. We
    present simple thermodynamic algorithms for (1) solving linear
    systems of equations, (2) computing matrix inverses, (3)
    computing matrix determinants, and (4) solving Lyapunov
    equations. Under reasonable assumptions, we rigorously establish
    asymptotic speedups for our algorithms, relative to digital
    methods, that scale linearly in matrix dimension. Our algorithms
    exploit thermodynamic principles like ergodicity, entropy, and
    equilibration, highlighting the deep connection between these two
    seemingly distinct fields, and opening up algebraic applications
    for thermodynamic computing hardware.

Comments: 21+15 pages, 7 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Emerging
          Technologies (cs.ET); Quantum Physics (quant-ph)
Cite as:  arXiv:2308.05660 [cond-mat.stat-mech]
          (or arXiv:2308.05660v1 [cond-mat.stat-mech] for this
          version)
          https://doi.org/10.48550/arXiv.2308.05660
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Gavin Crooks [view email]
[v1] Thu, 10 Aug 2023 16:01:07 UTC (4,248 KB)
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