UC Santa Barbara

Quantum computing is a revolutionizing technology on many fronts. Topological quantum computing is an especially attractive platform for this due to its innate robustness to local sources of noise and scalability. As the advent of quantum computing technologies nears, it becomes increasingly important to both optimize as much as possible the basic operations and to characterize them. In this thesis we study measurement-only topological quantum computing with Majorana zero mode (MZM) based qubits, particularly on their incarnation as the boudnary defects of $1d$ topological superconducting nanowires. The specific qubit device we consider are comprised of collections of such wires connected together on a single island such that 4 or 6 MZMs are hosted (tetron and hexon qubits respectively).

This thesis focuses on optimizing and characterizing the basic operations needed for quantum computing with such MZM qubits, concentrating on hexons which are the smallest MZM qubit allowing measurement-only gates on a single island. We begin by optimizing the Clifford gates for a single hexon qubit and for the controlled-Pauli, $\mathsf{W}$, and $\mathsf{SWAP}$ gates on two hexon qubits. A brute-force searched is performed with respect to a physically motivated example cost function. Tools and techniques are developed to aid in the compiling and optimization of measurement sequences. Utilizing the developed tools, we apply it towards the optimization of the stabilizer measurements for the surface code, an especially useful quantum error correcting code for the present MZM setting. Finally, we discuss adapting the technique of randomized benchmarking to the hexon setting, addressing simplifications and extensions that a hexon qubit can offer.