Controllable quantum systems that are shielded at a Hamiltonian level from the random fluctuations of their environments could provide a valuable resource for quantum information science. While these “protected qubits” promise unprecedentedly low error rates, this might come at the expense of ease of physical implementation. This thesis focuses on overcoming this apparent design problem in protected qubits within the context of superconducting circuits and their quantized electromagnetic fields. We describe some of the essential design tools: quantization of nonlinear lumped element circuits, approximation by an effective Hamiltonian, energy levels and matrix elements from numerical diagonalization, Hamiltonian verification via spectroscopy, and noise characterization using time-domain measurements. At each stage, examples are given from the following systems: the fluxonium artificial atom, the double fluxonium artificial molecule, and the cos2φ qubit. We validate the principle of designed protection with numerical predictions of the insensitivity of the cos2φ qubit to all expected decoherence mechanisms.
Thesis Advisor: Michel Devoret