Work in Progress: Exploring Ferroelectric Oscillators for Solving NP-Hard Problems Using Mallick's Coupling Mechanism

NP-hard problems pose a significant computational challenge for both classical and quantum computers, with no known efficient solution strategies. Recent research has explored networks of coupled oscillators as a promising analog alternative for solving such problems. While theoretically powerful, these systems remain difficult to implement in hardware and to map efficiently onto combinatorial problem structures. Recent models have provided a theoretical foundation for encoding optimization problems such as the Traveling Salesman Problem (TSP) into coupled oscillator dynamics. However, the lack of scalable, practical hardware platforms has limited experimental progress. In this work, we propose the use of silicon-compatible ferroelectric oscillators as a viable pathway toward physical implementation. We simulate the dynamics of coupled ferroelectric oscillators and validate their behavior by applying Mallick's coupling algorithm to TSP instances. Our preliminary results confirm the limit-cycle behavior predicted by Mallick's dynamic model and demonstrate the potential of implementing a system of ferroelectric coupled oscillators for solving NP-hard problems.