Floquet-Based Ising Machines Escape Local Minima in QUBO Problems

Solving large-scale Quadratic Unconstrained Binary Optimization (QUBO) problems is critical in various fields, including finance, physics, biology and engineering. However, these problems remain intractable on conventional computing architectures. As a result, 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 Ising Machines (IMs) aim to find the ground state of an Ising Hamiltonian, which encodes the solution to a QUBO problem. However, they rely on an energy minimization process based on gradient descent, making them inherently susceptible to getting trapped in local minima and, as a result, 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 Ising machines (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 problems’ solutions. As a result, the AFS significantly increases the likelihood of identifying accurate solutions compared to conventional PO-based IMs. More generally, this work establishes a new paradigm in analog computing that can be physically implemented using existing technologies across a variety of physical domains.