  The design of efficient quantum information processing will rely on optimal
nonequilibrium transitions of driven quantum systems. Building on a
recently-developed geometric framework for computing optimal protocols for
classical systems driven in finite-time, we construct a general framework for
optimizing the average information entropy for driven quantum systems.
Geodesics on the parameter manifold endowed with a positive semi-definite
metric correspond to protocols that minimize the average information entropy
production in finite-time. We use this framework to explicitly compute the
optimal entropy production for a simple two-state quantum system coupled to a
heat bath of bosonic oscillators, which has applications to quantum annealing.
