Relaxation processes in solid-state two-qubit gates

We consider a solid-state two-qubit gate subject to relaxation processes originated by transverse and longitudinal fluctuations of the single-qubit Hamiltonians. We model each noise component as a bosonic bath characterized by a specific power spectrum. We specialize our analysis to a i-SWAP gate implemented by Josephson qubits in a fixed coupling scheme. For high-frequency noise spectra extrapolated from single-qubit experiments we estimate the efficiency of the i-SWAP gate from the decay of anti-correlations between single-qubit switching probabilities.