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 (δRH,δRV), 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 δRV and δξ , while the dependence on δRH and δφ is approximately quadratic. As a practical result, the gate is much more sensitive to small errors in RV than in RH. 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%. It is also shown that the effects of different error sources are not independent of each other (linear error model). Under certain conditions, the deviation from the linear error model exceeds 10% of the total error. 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.
The errors in linear optics controlled not (C-NOT) gates are analyzed considering the polarization-dependent
phase sifts, in addition to the incorrectness of the beam splitting ratios. It is shown that the phase sifts at the
optical components is as crucial as other error sources discussed in the previous studies. Such a phase shift
unintentionally changes the linearly-polarized photons into a elliptically polarized ones. The operators for a
beam splitting device and the process matrix of the C-NOT operation including such errors are also given.