Analysis of experimental error sources in a linear-optics quantum gate

Abstract

Possible error sources in an experimentally realized linear-optics controlled-Z gate (Okamoto et al 2005 Phys. Rev. Lett. 95 210506) 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.