Fig. 6
From: Single-photon three-qubit quantum logic using spatial light modulators
Quantum-circuit representation and the measurement of operators for three-qubit gates. For the quantum gate in each panel, we present the quantum circuit, the 2D SLM phase required for implementing the gate, and the reconstructed transformation operator in the polarization-parity Hilbert space. a The identity gate \({{\Bbb I}_x} \otimes {{\Bbb I}_y}\); b \({\rm{CNO}}{{\rm{T}}_x} \otimes {{\Bbb I}_y}\); c \({{\Bbb I}_x} \otimes {\rm{CNO}}{{\rm{T}}_y}\); d \({\rm{CNO}}{{\rm{T}}_x} \otimes {\rm{CNO}}{{\rm{T}}_y}\); e a rotation R x (Ï€) on the x-parity qubit and a rotation R y \(\left( {\frac{\pi }{2}} \right)\) on y-parity qubit, corresponding to the separable quantum gate \({\rm{CNO}}{{\rm{T}}_x} \otimes \sqrt {{\rm{CNO}}{{\rm{T}}_y}} \); and f a joint rotation R xy \(\left( {\frac{\pi }{2}} \right)\) in the joint Hilbert space of x- and y-parity
