We propose an algorithm inspired by optical coherent Ising machines to solve the problem of polynomial unconstrained binary optimisation (PUBO). We benchmark the proposed algorithm against existing PUBO algorithms on the extended Sherrington-Kirkpatr
ick model and random third-degree polynomial pseudo-Boolean functions, and observe its superior performance. We also address instances of practically relevant computational problems such as protein folding and electronic structure calculations with problem sizes not accessible to existing quantum annealing devices. In particular, we successfully find the lowest-energy conformation of lattice protein molecules containing up to eleven amino-acids. The application of our algorithm to quantum chemistry sheds light on the shortcomings of approximating the electronic structure problem by a PUBO problem, which, in turn, puts into question the applicability of quantum annealers in this context.
Quantum simulators and processors are rapidly improving nowadays, but they are still not able to solve complex and multidimensional tasks of practical value. However, certain numerical algorithms inspired by the physics of real quantum devices prove
to be efficient in application to specific problems, related, for example, to combinatorial optimization. Here we implement a numerical annealer based on simulating the coherent Ising machine as a tool to sample from a high-dimensional Boltzmann probability distribution with the energy functional defined by the classical Ising Hamiltonian. Samples provided by such a generator are then utilized for the partition function estimation of this distribution and for the training of a general Boltzmann machine. Our study opens up a door to practical application of numerical quantum-inspired annealers.
