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We have analyzed and proposed coupling mechanisms between Three JosephsonJunction Flux Qubits (3JJQ). For this, we have developed a numerical method toextract the effective Hamiltonian of a system of coupled qubits via theSchrieffer-Wolff transformation (SWT). We then give a comprehensiveintroduction to the 3JJQ, and study it analytically by approximating itspotential with a Harmonic well. With a clear understanding of the 3JJQs, we usethe SWT to gain intuition about their effective dipolar interaction with theelectromagnetic field, and use that intuition to propose and study analyticallyand numerically the capacitive coupling of two 3JJQs via a non-tunablecapacitor, and the inductive coupling of two 3JJQs via a tunable JosephsonJunction (dc-SQUID), showing that we are able to reproduce non-stoquasticHamiltonians in the strong-coupling regime.

Design of Novel Coupling Mechanisms between Superconducting Flux Qubits