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Correlated flux noise and decoherence in two inductively coupled flux qubits

We have studied decoherence in a system where two Josephson-junction flux qubits share a part of their superconducting loops and are inductively coupled. By tuning the flux bias condition, we control the sensitivities of the energy levels to flux noises in each qubit. The dephasing rate of the first excited state is enhanced or suppressed depending on the amplitudes and the signs of the sensitivities. We have quantified the $1/f$ flux noises and their correlations and found that the dominant contribution is by local fluctuations.