Utilizing Quadratic Unconstrained Binary Optimization problem for simulating dynamics of quantum system

We introduce a novel approach to simulate dynamical (linear) systems (quantum or otherwise) parallel in time using quantum annealers. In particular,  we describe how the solution state vector can be found by solving a specifically crafted system of linear equations. Moreover, we demonstrate that such systems can, in fact, be effectively solved (up to a given precision) with Quadratic Unconstrained Binary Optimization. This naturally leads to a class of hybrid classical-quantum algorithms that can be implemented and executed on near-term quantum annealers.