Quantum optimal control of superconducting circuits

Quantum technologies require high-fidelity processes and transformations. Quantum optimal control allows finding optimal strategies to drive quantum systems with precisions compatible with the fault tolerant threshold even in presence of moderate levels of leakage and noise, provided that faithful simulation methods are available. We review efficient algorithms to simulate and optimally control few- and many-body quantum dynamics and present an information theoretical analysis of quantum optimal control processes, highlighting the potential applications and the limits of optimal control methods arising from geometrical, energetic and information arguments. We finally review some theoretical and experimental applications of optimal control, ranging from the optimal control of circuit QED systems to optimal quantum annealing, an annealing process that goes beyond the adiabatic strategy.