Floquet-Based Ising Machines Escape Local Minima in QUBO Problems
Nicolas Casilli, Seunghwi Kim, Sunil Mittal, Marvin Onabajo, Andrea Alù, Cristian Cassella · Physical Review X · 2026
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.