  Time-bin qubits, where information is encoded in a single photon at different
times, have been widely used in optical fiber and waveguide based quantum
communications. With the recent developments in distributed quantum
computation, it is logical to ask whether time-bin encoded qubits may be useful
in that context. We have recently realized a time-bin qubit controlled-phase
(C-Phase) gate using a 2 X 2 optical switch based on a lithium niobate
waveguide, with which we demonstrated the generation of an entangled state.
However, the experiment was performed with only a pair of input states, and
thus the functionality of the C-Phase gate was not fully verified. In this
research, we used quantum process tomography to establish a process fidelity of
97.1%. Furthermore, we demonstrated the controlled-NOT gate operation with a
process fidelity greater than 94%. This study confirms that typical two-qubit
logic gates used in quantum computational circuits can be implemented with
time-bin qubits, and thus it is a significant step forward for realization of
distributed quantum computation based on time-bin qubits.
