A geometric approach to dynamically corrected gates

Future technologies such as quantum computing, sensing and communication demand the ability to control microscopic quantum systems with unprecedented accuracy. This task is particularly daunting due to unwanted and unavoidable interactions with noisy environments that destroy quantum information through decoherence. I will present recent progress in understanding and modeling the effects of noise on the dynamics of a qubit and show how this can be used to develop new ways to slow down decoherence. I will then describe a new general theory for dynamically combatting decoherence by driving qubits in such a way that noise effects destructively interfere and cancel out. This theory exploits a rich geometrical structure hidden within the time-dependent Schrödinger equation.