Quantum Optimal Control of Lambda System Ensembles

In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration, where two lower stable energy levels are indirectly coupled via a higher unstable energy level. We study the optimal state transfer in a three-level Lambda system using a density-matrix formulation that allows for mixed states. The aim is to carry out transfer between two desired states while minimizing both the energy of controls and occupation in the higher energy state, which is most susceptible to decoherence. By combining geometric control methods with the Pontryagin Maximum Principle and symmetry reduction techniques, we can enable low-decoherence, faster gate operations, whilst optimizing for energy-efficient controls. To illustrate our techniques, we carry out numerical simulations for a Hadamard-like transformation.