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  • Open Access

Ising Machine by Dimensional Collapse of Nonlinear Polarization Oscillators

Salvatore Chiavazzo1, Marcello Calvanese Strinati2, Claudio Conti3, and Davide Pierangeli3,1,*

  • *Contact author: davide.pierangeli@roma1.infn.it
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Phys. Rev. Lett. 135, 063801 – Published 4 August, 2025

DOI: https://doi.org/10.1103/qs29-2xqc

Abstract

Ising machines show promise as ultrafast hardware for optimizations encoded in Ising Hamiltonians but fall short in terms of success rate and performance scaling. Here, we propose a novel Ising machine that exploits the three-dimensional nature of nonlinear polarization oscillators to counteract these limitations. Based on the evolution of the optical polarization in third-order nonlinear media, the high-dimensional machine reaches the Ising ground state by the mechanism of “dimensional collapse”: the dynamics on the Poincaré sphere undergoes a self-induced collapse into polarization fixed points mapping an Ising spin. Collapse from a spherical to a binary spin occurs when the polarization oscillator experiences iterative loss and anisotropic feedback. The photonic setup consists of polarization modulated pulses in a χ(3) crystal subject to measurement and feedback. We numerically demonstrate the polarization machine achieves enhanced success probability on benchmark graphs and an exponential improvement in performance scaling with respect to coherent Ising machines due to its high-dimensional operation. The proposed Ising machine paves the way for a new class of Ising solvers with enhanced computing capabilities.

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Phys. Rev. Lett. 135, 063801– Published 4 August, 2025
  • Received 4 April 2025
  • Revised 22 June 2025
  • Accepted 9 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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