Hybrid Quantum Algorithms for N-Body Simulations

N-body simulations is a fundamental problem in molecular dynamics. For example, N-body simulations can be employed to study powder flow. It is worth noting that powder or granular materials are the second ubiquitous substance in the industry after water. Numerous sequential and parallel algorithms have been proposed in the literature for N-body simulations on classical computers. Given a set of n particles in a d-dimensional space, a brute force algorithm will take Ω(n²d) time to simulate each step of this system of particles. Numerous algorithms in the literature perform better than this under some suitable assumptions. Given the potential speedups offered by quantum computing, an interesting open problem is to investigate how much speedups can be obtained for N-body simulations using quantum computers. In this paper we present efficient algorithms that run on quantum-classical hybrid models of computing. Specifically, our algorithms solve the problem of finding close neighbors using a quantum computer and the other steps on a Parallel Random Access Machine (PRAM). Our quantum algorithms outperform other algorithms in the literature asymptotically as well as on empirical evaluations.