Using Quantum Computers to Study Random Close Packing of Granular Discs

We reformulate the problem of granular random close packing of 2D discs as a Quadratic Unconstrained Binary Optimization in order to utilize the D-Wave 2000Q quantum annealing computer. The solution is a set of ground states corresponding to jammed configurations in which no single particle can be moved without creating a non-zero potential. The problem is adapted to the quantum computer by discretizing space and mapping each point onto physical quantum-bits (qubits). An objective function is derived that defines the system energy for arbitrary particle locations, subject to constraints biasing solutions toward a pre-determined number of particles. Uniquely, the quantum computer samples and returns minimum values of this function finding low energy states, a subset of which are physically realizable solutions we seek. While quantum computing's technological infancy restricts our study to proof-of-concept, our work still shows promise for efficient analysis of complex granular problems.