Implementing a Linear Optical CNOT, AND, and a Half Adder by Using the Polarization and the Spatial Mode of Light

There has been great interest in the development of all optical logic gates in relation to optical computing and quantum computers. Many optical logic gate systems using optical-fiber and semiconductor devices [1–7], which mostly use fast pulses for rapid communication, have been developed. These systems use nonlinear optical devices, which require high light intensity, which is not suitable for quantum computation [8]. Optical logic gates that can operate in a single-photon level are studied for quantum computation. A universal quantum computation can be performed using a single-qubit rotation and two-qubit controlled-NOT (CNOT) operations [9]. It has also been shown that universal quantum computation can be performed using only linear optical elements and single photon detectors [10]. Several proposals for two-photon controlled logic gates were presented [11,12] and experimentally demonstrated [13]. However, most of those schemes require post selection of measurement results, and the gates operate probabilistically. Recent studies have shown that two different qubits can be encoded to a photon by using polarization and spatial mode degrees of freedom, and logic gates can be constructed by using this feature [14,15]. Such a system is known not to be scalable, but these quantum gates operate deterministically. Until now, these studies have been limited to the implementation of single gates such as CNOT gate. In this work, we show how to construct an AND gate, as well as a CNOT gate, by using the polarization and the spatial mode as qubits and how to construct a half-adder by combining these two gates.