availability of single-qubit operations. However, it is difficult to realize the necessary two-qubit operations since the physical interaction between photons is very small. Linear optics quantum computation [@klm] and nonlinear optical processes involving few photons have been proposed to circumvent this problem. The first is a probabilistic scheme implicitly based on the nonlinearity hidden in single-photon detectors, while the second is based on the enhancement of photon-photon interaction either in cavity QED configurations [@turch] or in dense atomic media exhibiting electromagnetically induced transparency (EIT) [@eit]. In this latter case, optical nonlinearities can be produced when EIT is disturbed, either by introducing additional energy level(s) [@Schmidt96; @Wang01], or by mismatching the probe and control field frequencies [@Grangier98; @Matsko03].

The scope of this paper is to assess the performance of a two-qubit quantum phase gate (QPG) for travelling single photon qubits [@Lukin00; @Ottaviani03; @Petrosyan02; @tripod; @Masalas04], based on the cross-Kerr nonlinearity which is generated in a five-level atomic medium. In a QPG, one qubit gets a phase conditional to the other qubit state according to the transformation [@Lloyd95; @NielsenChuang] $|i\rangle _{1}|j\rangle _{2} \rightarrow
\exp\left\{i \phi_{ij} \right\}|i\rangle _{1}|j\rangle _{2} $ where $\{i,j\}=0,1$ denote the logical qubit bases. This gate is universal when the 