Abstract for Talk 1: In this work, we present a super-polynomial improvement in the precision scaling of quantum simulations for coupled classical-quantum systems. Such systems are found, for example, in molecular dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman-von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a super-polynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density.

Abstract for Talk 2: One of the most promising applications of quantum computing is the simulation of quantum systems. The goal is to construct a quantum algorithm that closely approximates the solution to Schrödinger’s equation, which is a unitary propagator in time. Much attention has been given to this problem, and modern approaches provide a variety of highly efficient algorithms. The lesser-studied Lindblad equation generalizes the Schrödinger equation to quantum systems that undergo dissipation, leading to non-unitary dynamics that prevent a naïve application of state-of-the-art quantum algorithms. In this work, we utilize a correspondence between repeated interaction CPTP maps and Lindbladian dynamics to formulate an embedding of the non-unitary dynamics in a higher dimensional space that evolves under a Hamiltonian with low space overhead, which we can simulate with efficient quantum algorithms. In the process, we derive error bounds on the approximate correspondence and provide bounds on the computational complexity of the approach.