  We investigate the propagation of microwave photons in a one-dimensional open
waveguide interacting with a number of artificial atoms (qubits). Within the
formalism of projection operators and non-Hermitian Hamiltonian approach we
develop a one-photon approximation scheme for the calculation of the
transmission and reflection factors of the microwave signal in a waveguide
which contains an arbitrary number \emph{N} of non-interacting qubits. We
considered in detail the resonances and photon mediated entanglement for two
and three qubits in a chain. We showed that in non Markovian case the resonance
widths, which define the decay rates of the entangled state, can be much
smaller than the decay width of individual qubit. It is also shown that for
identical qubits in the long wavelength limit a coherent superradiant state is
formed with the width being equal to the sum of the widths of spontaneous
transitions of \emph{N} individual qubits. The results obtained in the paper
are of general nature and can be applied to any type of qubits. The specific
properties of the qubit are only encoded in the two parameters: the qubit
energy $\Omega$ and the rate of spontaneous emission $\Gamma$.
