Controlling Error-Correctable Bosonic Qubits
The harmonic oscillator is a ubiquitous system in physics, describing a wide range of phenomena, both classically and quantum mechanically. While oscillators are relatively straightforward to control classically, they present much more of a challenge in the quantum realm where such systems, modelled as Bosonic modes, have many more degrees of freedom. Controlling Bosonic modes is a crucial task in light of proposals to use these systems to encode quantum information in a way which is protected from noise and dissipation. In this thesis a variety of approaches to controlling such systems are discussed, particularly in the superconducting microwave domain with cavity resonators. In the first part, an experiment demonstrates how a simple dispersively coupled auxiliary system results in universal control, and therefore allows the synthesis of arbitrary manipulations of the system. This approach is employed to create and manipulate states which constitute an error-correctable qubit. The main drawback of this approach is the way in which errors and decoherence present in the auxiliary system are inherited by the oscillator. In the second part, I show how these effects can be suppressed using Hamiltonian engineering to produce a simple form of first-order ”fault-tolerance.” This approach allows us to demonstrate versions of cavity measurements and manipulations which are protected from dominant error mechanisms.