We study the effects of correlated low frequency noise sources acting on a two qubit gate in a fixed coupling scheme. A phenomenological model for the spatial and cross-talk correlations is introduced. The decoherence inside the SWAP subspace is analysed by combining analytic results based on the adiabatic approximation and numerical simulations. Results critically depend on amplitude of the low frequency noise with respect to the qubits coupling strength. Correlations between noise sources induce qualitative different behaviors depending on the values of the above parameters. The possibility to reduce dephasing due to correlated low frequency noise by a recalibration protocol is discussed.
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