In our earlier work we posited that simple quantum gates and quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photons transverse linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of linear optical quantum computing (LOQC) within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate; and second, photon entanglement can be encoded as a superposition state of a single photon in a higher-dimensional state space afforded by LM. We describe here our experimental results for construction a controlled NOT (CNOT) gate logic within a holographic medium, and present the quantum state tomography for this device. Our theoretical and numerical results indicate that OptiGrates photo-thermal refractive (PTR) glass is an enabling technology. This work has been grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We discuss the strengths (high efficiencies, robustness to environment) and limitations (scalability, crosstalk) of this technology. While not scalable, the utility and robustness of such optical elements for broader quantum information processing applications can be substantial.
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