Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. In this Letter, we combine these two approaches to study the dynamicsof a superconducting phase qubit. We experimentally demonstrate Landau-Zener interferometry based on the pure geometric phases in this solid-state qubit. We observe the interference caused by a pure geometric phase accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is canceled out by a spin-echo pulse. The full controllability of the qubit state as a function of the intrinsically robust geometric phase provides a promising approach for quantum state manipulation.
We propose a scheme to clarify the coupling nature between superconducting
Josephson qubits andmicroscopic two-level systems. Although dominant interest
in studying two-level systemswas in phase qubits previously, we find that the
sensitivity of the generally used spectral method in phase qubits is not
sufficient to evaluate the exact form of the coupling. On the contrary, our
numerical calculation shows that the coupling strength changes remarkably with
the flux bias for a flux qubit, providing a useful tool to investigate the
coupling mechanism between the two-level systems and qubits.
A composite system of Majorana-hosted semiconductor nanowire and
superconducting flux qubit is inves- tigated. It is found that the coupling
between these two subsystems can be controlledelectrically, supplying a
convenient method to implement {pi}/8 phase gate of a Majorana-based
topological qubit. We also present a scheme to transfer information from the
flux qubit to the topological qubit using Landau-Zener transition. In addition,
a structure named top-flux-flux is proposed to retrieve the information stored
in the topological qubit. With the demonstration of the entanglement of two
topological qubits, it is very promising to do quantum information process with
this hybrid system.