Three-Josephson junctions flux qubit couplings

We analyze the coupling of two flux qubits with a general many-body projector into low-energy subspace. Specifically, we extract effective Hamiltonians that controls dynamics when they are coupled via capacitor and/or Josephson junction. While induces static charge tunable by design, junction produces magnetic-like interaction easily replacing superconducting quantum interference device. Those elements allow to engineer XX, YY, and ZZ interactions, including ultrastrongly ones. present an exhaustive numerical study for three-Josephson junctions qubit can be directly used in experimental work. The method developed here, namely, tool at strong coupling, applied replicate our analysis systems many any type coupling.