Developing and using optimal control methods for experimental robustness

Abstract

This thesis details work performed on the improvement of experimental control of quantum systems through the use of optimal control theory. We pursue this objective through both conceptual and practical routes. We first devise improved methods of optimal control for quantum systems. We then apply them, as well as more established methods, to experimental situations where robustness to inaccuracy and error is sought. We develop a method for improving the computational efficiency of optimal control theory in the context of quantum control. This approach makes use of the iterative nature of optimisation algorithms, by using perturbation theory to minimise the effort needed to calculate the time propagator associated with a controlled Hamiltonian. We also create a new way of defining a figure of merit when optimising for robustness against error in an experiment. This method specifically applies to errors that have a relatively small effect on the controlled system's Hamiltonian. We compare this with an ensemble method based around randomly sampling several points on the control landscape, and find these methods to be largely equivalent for small errors, with the ensemble method being superior for larger error. On the applied side, we design radio frequency magnetic pulses that create robustness in spin ensembles to inhomogeneous broadening and variations of coupling strength to the control field for two applications. In the first, we create reliable gates in a situation where limitations are imposed on the control that can be applied. In the second application, we design controls for radio frequency magnetic pulses to create a superradiant state in a spin ensemble. Finally, we collaborate with the experiment to measure the electrons electric dipole moment that is being performed at Imperial College London. For this collaboration, we shape the envelope of the radio frequency control pulses used in the experiment to create superpositions of Zeeman and Stark-shifted excited states in YbF molecules. This shaping allows us to impart pre-determined phases to these superpositions, in a manner that is robust to errors in the control pulse envelope. We obtain sets of robust and sensitive pulses that have been sent to the experiment for testing purposes.