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.
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