Optimal protocols for slowly driven quantum systems

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 semidefinite 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.

Figure 1

Plot of ${\langle {\mathrm{\Sigma }}_I\rangle }_{{\mathbf{\Lambda }}_{\text{opt}}}/{\langle {\mathrm{\Sigma }}_I\rangle }_{{\mathbf{\Lambda }}_{\text{opt}},0}$ where ${\langle {\mathrm{\Sigma }}_I\rangle }_{{\mathbf{\Lambda }}_{\text{opt}},0}$ is the optimal average entropy for ${\gamma }_0=1,{\gamma }_1=0$.