Qubit dynamics under alternating controls

Abstract

In this thesis, we discuss two problems of quantum dynamics in the presence of alternating controls. Alternating controls arise in many protocols designed to extend the duration over which a qubit is a useful computational resource. This is accomplished by control sequences that either retard decoherence, or that accomplish a quantum operation in as short a time as possible. The first problem tackles the use of a composite-pulse control sequence known as 'rotary-echo' for quantum magnetometry purposes. The sequence consists in the continuous drive of a qubit, with field phases that alternate at specific intervals. We implement such a magnetometry protocol using an electronic qubit in diamond, and experimentally confirm the flexibility yielded by the tuning of sequence parameters that achieves a good compromise between decoherence resilience and sensitivity. The second problem theoretically investigates the time-optimal evolution of a qubit in the case of a restricted control set composed of alternating rotations around two non-parallel axes on the Bloch sphere. Using accessible algebraic methods, we show that experimental parameters, such as the angle between the two rotation axes, restrict the necessary structure of time-optimal sequences. We propose to implement such an evolution through alternate driving as an advantageous alternative to the slow, noisy direct addressing of a nuclear qubit anisotropically hyperfine-coupled to an electronic spin in diamond.