UC Santa Barbara

A key milestone on the path towards building a quantum computer will be the demonstration of an algorithm which exceeds the capabilities of any classical computer - achieving so called quantum supremacy. The challenge in developing such an algorithm lies in balancing computational complexity with experimental feasibility, particularly in the presence of errors. In this thesis, we design superconducting qubits and algorithms with the goal of finding such a balance. We implement a wide variety of control protocols, including parametric drive, adiabatic control, floquet evolution and time-domain spectroscopy. These tools are used to the study topological invariants, quantum chaos, quantum statistical mechanics, chiral symmetry breaking and many-body localization. We present experimental techniques for characterizing the complexity and fidelity of these algorithms and show that quantum supremacy is achievable using existing technology.