Nonadiabatic Parametric Control Through the Lens of Landau-Zener Interference and Resonant Driving

Nonadiabatic parametric control enables the introduction of arbitrary phases to single-qubit driving and qubit-qubit couplings, which can be leveraged to achieve fast, high fidelity single- and two-qubit gates. Arbitrary phases are also an essential ingredient for certain analog quantum simulation experiments. We can view the dynamics induced by nonadiabatic parametric control through several lenses. In the time domain, longitudinal modulation in the vicinity of an avoided crossing induces coherent Landau-Zener interference, whereas in the frequency domain, resonant parametric modulation induces a swapping interaction. We also discuss these periodically driven dynamics in the Floquet picture for both longitudinal and transverse driving. We explore the implications of these two driving schemes for adiabatic state preparation, an essential step towards simulating topological phases of matter like fractional quantum Hall.