A real-time path integral representation of driven quantum algorithms

Both adiabatic quantum computing / quantum annealing and the quantum approximate optimization algorithm combine a problem Hamiltonian with a non-commuting driver Hamiltonian in order to efficiently explore the complete state space of an optimization problem. We develop a representation of such algorithms as a real-time path integral that directly and rigorously implements the otherwise colloquial idea that quantum algorithms follow all possible computations at the same time. We apply path integral techniques such as eikonals and semiclassics in order to provide a way to better understanding under which conditions we can expect these algorithms to reliably converge.