Possible error sources in an experimentally realized linear-optics controlled-Z gate are analyzed by considering the deviations of the beam splitting ratios from the ideal values (δR_H, δR_V), the polarization-dependent phase shift (birefringence) of the optical components (δΦ), and the mode mismatch of input photons (δξ). It is found that the error rate is linearly dependent on δR_V and δξ, while the dependence onδR_H and δΦ is approximately quadratic. As a practical result, the gate is much more sensitive to small errors in R_V than in R_H. Specifically, the reflectivity error for vertical polarization must be less than 0.1% to realize a gate with an error of less than 0.1%, whereas the reflectivity error for horizontal polarization can be up to 1%. The method of analysis used illustrates the basic features of errors in general linear optics quantum gates and circuits, and can easily be adapted to any other device of this type.
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