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Floquet-Based Ising Machines Escape Local Minima in QUBO Problems

Nicolas Casilli1, Seunghwi Kim2, Sunil Mittal1, Marvin Onabajo1, Andrea Alù3,4, and Cristian Cassella1,*

  • *Contact author: c.cassella@northeastern.edu
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Phys. Rev. X 16, 031010 – Published 17 July, 2026

DOI: https://doi.org/10.1103/kgfb-5g2w

Abstract

Solving large-scale quadratic unconstrained binary optimization (QUBO) problems is critical in various fields, including physics, finance, and engineering. However, these problems remain intractable on conventional computing architectures. Alternative solvers, such as Ising machines (IMs) based on networks of coupled electronic, mechanical, or photonic parametric oscillators (POs), have recently been developed. PO-based IMs aim to find the ground state of an Ising Hamiltonian, which encodes the solution to a QUBO problem. However, their analog nature and their energy-minimization process based on gradient descent make PO-based IMs inherently susceptible to identifying inaccurate solutions. In this work, we introduce and validate a QUBO solver—the analog Floquet solver (AFS)—which enhances the dynamics of PO-based IMs by leveraging Floquet states that emerge spontaneously in POs coupled to high-quality-factor resonances. These states enable the AFS to embed periodic time modulation into its energy-minimization process, allowing it to escape local minima during the search for QUBO problem solutions. As a result, the AFS significantly increases the likelihood of identifying accurate solutions compared to conventional PO-based IMs. More generally, this work defines a new paradigm in analog computing—spanning both classical and quantum realms—that can be physically realized with existing technologies across diverse physical domains.

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Popular Summary

Ising machines, implemented as dynamical systems featuring a network of coupled parametric oscillators representing artificial Ising spins, are promising analog computing platforms capable of quickly and efficiently solving quadratic unconstrained binary optimization (QUBO) problems. However, many such Ising machines are prone to become trapped in local minima during their energy minimization process, leading them to often produce suboptimal solutions to the QUBO problems. To address this, Floquet amplitude modulations are dynamically activated in the artificial Ising spins by strongly coupling an external resonant mode to each parametric oscillator. These modulations enable the dynamical system, dubbed an analog Floquet solver, to escape from local minima and consequently reach more optimal solutions than the ones achieved by the parametric oscillator-based Ising machine counterpart. Because of the generality of the approach to activate Floquet modulations in parametric oscillator-based artificial Ising spins, analog Floquet solvers can be easily implemented across many possible physical domains.

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Phys. Rev. X 16, 031010– Published 17 July, 2026
  • Received 3 October 2025
  • Accepted 12 June 2026
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