Qubits protected against noise have long coherence times and can be used as basic components in quantum computers. This thesis studies two distinct superconductor-based qubit platforms that realize noise-protection in different ways.

The first part of the thesis is concerned with Majorana zero modes that are non-Abelian anyons predicted to exist at the boundary of certain topological superconductors. Symmetries of the topological superconductor protect Majorana zero modes from decoherence and allow for nonlocal encoding of quantum information which is insensitive to local noise. We study a Majorana system where single electron charge-transfer between external quantum dots and the Majorana system realizes a universal gate set. We study non-idealities of the charge-transfer operations and propose a minimal experiment that can demonstrate Majorana non-Abelian properties.

The second part of the thesis is concerned with superconducting qubits based on conventional superconductors. These qubits are micrometer-sized superconducting circuits that are sensitive to the electromagnetic environment. Despite inherent noise sensitivity, superconducting qubits are promising as a platform to realize large-scale quantum computers. We study two ways superconducting qubits can be engineered to reduce noise sensitivity.

First, we consider a flux qubit that is protected against relaxation by separating its quantum states in different potential wells. We devise a universal gate scheme that momentarily reduces the level of protection to partially hybridize the qubit states, enabling direct-drive microwave gates. We also consider a readout scheme that preserves protection by reading out via an auxiliary qubit mode.

Second, we consider protection against flux noise which can be achieved using superinductors. We consider a junction array superinductor comprised of quartons that exhibits a quartic energyphase relation, effectively increasing the inductance. We study non-idealities in the quarton array and compare it to conventional junction array superinductors. We use the quarton array superinductor as the inductive elements in the 0 − π qubit, the bifluxon qubit, and the Blochnium qubit and numerically evaluate dephasing times due to flux noise. Finally, we discuss the experimental requirements needed to achieve protection against flux noise in superconducting qubits based on quarton array superinductors.