Charge-Density-Wave Oscillator Networks for Solving Combinatorial Optimization Problems

Abstract

Many combinatorial optimization problems fall into the non-polynomial time NP-hard complexity class, characterized by computational demands that increase exponentially with the size of the problem in the worst case. Solving large-scale combinatorial optimization problems efficiently requires novel hardware solutions beyond the conventional von Neumann architecture. We propose an approach for solving a type of NP-hard problem based on coupled oscillator networks implemented with charge-density-wave condensate devices. Our prototype hardware, based on the 1T polymorph of TaS2, reveals the switching between the charge-density-wave electron-phonon condensate phases, enabling room-temperature operation of the network. The oscillator operation relies on hysteresis in current-voltage characteristics and bistability triggered by applied electrical bias. This work presents a network of injection-locked, coupled oscillators whose phase dynamics follow the Kuramoto model and demonstrates that such coupled quantum oscillators naturally evolve to a ground state capable of solving combinatorial optimization problems. The coupled oscillators based on charge-density-wave condensate phases can efficiently solve NP-hard Max-Cut benchmark problems, offering advantages over other leading oscillator-based approaches. The nature of the transitions between the charge-density-wave phases, distinctively different from resistive switching, creates the potential for low-power operation and compatibility with conventional Si technology.