  The controlled generation of entangled states of two quantum bits is a
fundamental step toward the implementation of a quantum information processor.
In nano-devices this operation is counteracted by the solid-state environment,
characterized by a broadband and non-monotonic power spectrum, often 1/f at low
frequencies. For single-qubit gates, incoherent processes due to fluctuations
acting on different time scales result in peculiar short- and long-time
behavior. Markovian noise gives rise to exponential decay with relaxation and
decoherence times, T1 and T2, simply related to the symmetry of the
qubit-environment coupling Hamiltonian. Noise with the 1/f power spectrum at
low frequencies is instead responsible for defocusing processes and algebraic
short-time behavior. In this paper, we identify the relevant decoherence times
of an entangling operation due to the different decoherence channels
originating from solid-state noise. Entanglement is quantified by concurrence,
which we evaluate in an analytic form employing a multi-stage approach. The
'optimal' operating conditions of reduced sensitivity to noise sources are
identified. We apply this analysis to a superconducting \sqrt{i-SWAP} gate for
experimental noise spectra.
