Geometric framework for noise-resistant quantum control

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 a new theoretical framework for deriving control waveforms that dynamically combat 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 in which quantum evolution is mapped to geometric curves. Control waveforms that suppress noise can be obtained by drawing closed curves and computing their curvatures. I will show how this can be done for single- and multi-qubit systems.