Design of an inductively shunted transmon qubit with tunable transverse and longitudinal coupling

This thesis is set in the framework of superconducting transmon-type qubit architectures with special focus on two important types of coupling between qubits and harmonic resonators: transverse and longitudinal coupling. We will see that longitudinal coupling offers some remarkable advantages with respect to scalability and readout. This thesis will focus on a design, which combines both these coupling types in a single circuit and provides the possibility to choose between pure transverse and pure longitudinal or have both at the same time. We will start with an introduction to circuit quantization, where we will explain how to describe and analyze superconducting electrical circuits in a systematic way and discuss which characteristic circuit elements make up qubits and resonators. We will then introduce the two types of coupling between qubit and resonator which are provided in our design. Translating this discussion from the Hamiltonian level to the language of circuit quantization, we will show how to design circuits with specifically tailored couplings. We will focus on our circuit design that consists of an inductively shunted transmon qubit with tunable coupling to an embedded harmonic mode. The distinctive feature of the tunable design is that the transverse coupling disappears when the longitudinal is maximal and vice versa. Subsequently, we will turn to the implementation of our circuit design, discuss how to choose the parameters, and present an adapted alternative circuit, where coupling strength and anharmonicity scale better than in the original circuit. In addition, we present a proposal for an experimental device that will serve as a prototype for a first experiment. We will conclude the thesis discussing different possibilities to do readout with our circuit design, including a short discussion of the influence of dissipation.