Pith. sign in

REVIEW 1 cited by

Thermodynamic Linear Algebra

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2308.05660 v2 pith:3VE7ZBZQ submitted 2023-08-10 cond-mat.stat-mech cs.ETquant-ph

classification cond-mat.stat-mechcs.ETquant-ph
keywords computinglinearthermodynamicalgebraalgorithmsmatrixsolvingaccelerating
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original 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.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation

    cs.LG 2025-07 conditional novelty 4.0 of 10

    Under a small-angle approximation, the stationary phase covariance of a noisy Kuramoto oscillator network equals the inverse of the encoded matrix up to known constants.

Pith tools