Optimal control of a qubit coupled to a two-level fluctuator

A central challenge for implementing quantum computing in the solid state is decoupling the qubits from the intrinsic noise of the material. We investigate limits of controllability for a paradigmatic model: A single qubit coupled to a two-level fluctuator exposed to a heat bath. We systematically search for optimal pulses using a generalization of the novel open system Gradient Ascent Pulse Engineering (GRAPE) algorithm. We show and explain that next to the known optimal bias point of this model, there are optimal shapes which refocus unwanted terms in the Hamiltonian. We study the limitations of control set by the decoherence properties in the fast flipping regime, which go beyond a simple random telegraph noise model. This can lead to a significant improvement of quantum operations in hostile environments