Scaling advantage of chaotic amplitude control for high-performance combinatorial optimization

The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to transform our ability to understand and control complex systems. However, most of the physical implementations of such machines have been based on a similar concept that is closely related to relaxational dynamics such as in simulated, mean-field, chaotic, and quantum annealing. Here we show that dynamics that includes a nonrelaxational component and is associated with a finite positive Gibbs entropy production rate can accelerate the sampling of low energy states compared to that of conventional methods. By implementing such dynamics on field programmable gate array, we show that the addition of nonrelaxational dynamics that we propose, called chaotic amplitude control, exhibits exponents of the scaling with problem size of the time to find optimal solutions and its variance that are smaller than those of relaxational schemes recently implemented on Ising machines. Finding the ground state of a variety of complex systems can be formulated as the minimization of the total interaction energy of Ising machines, posing a challenge as computational cost increases exponentially with system size. In this paper, the authors propose an algorithm to find the ground states of Ising-type problems by destabilising non-trivial attractors in combinatorial optimisation solvers through a heuristic modulation of the target amplitude, and show that this provides an improved scaling with respect to several existing methods.