Quantum-inspired encoding enhances stochastic sampling of soft matter systems

Sampling polymer melts remains a paradigmatically hard problem in computational physics, despite the various ingenious Monte Carlo and Molecular strategies that have been developed so far. Achieving an efficient and unbiased sampling of densely packed polymers is hard even in the minimalistic case of crossable polymers on a lattice. Here we tackle the problem from a novel perspective, namely by using a quadratic unconstrained binary optimization (QUBO) model to generate systems of self-assembling ring polymers on arbitrary lattices (regular or not). The QUBO model naturally lends to imposing various physical constraints that would otherwise be difficult to handle with conventional MC and MD schemes. These constraints include fixing the packing density (lattice filling fraction), contact energy, and bending energy (curvature) of the system. This facile handling of multiple physical constraints enables the study of properties not addressed before, as we demonstrate by computing the overall entanglement properties of self-assembling rings. Finally, the model is amenable to being implemented on quantum machines that, in the case of D-Wave quantum annealers can speed up sampling by orders of magnitudes. In the end, I will discuss how QUBO-based sampling can be generalized to address canonically-equilibrated melts of rings with arbitrary bending rigidity.