Large scale quantum computers will consist of many interacting qubits. In this paper we expand the two flux qubit coupling scheme first devised in [Phys. Rev. B {bf 70}, 140501 (2004)] and realized in [Science {bf 314}, 1427 (2006)] to a three-qubit, two-coupler scenario. We study L-shaped and line-shaped coupler geometries, and show how the interaction strength between qubits changes in terms of the couplers dimensions. We explore two cases: the on-state where the interaction energy between two nearest-neighbor qubits is high, and the off-state where it is turned off. In both situations we study the undesirable crosstalk with the third qubit. Finally, we use the GRAPE algorithm to find efficient pulse sequences for two-qubit gates subject to our calculated physical constraints on the coupling strength.
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