  Geometrical frustration in correlated systems can give rise to a plethora of
novel ordered states and intriguing phases. Here, we analyze theoretically
vertex-sharing frustrated Kagome lattice of Josephson junctions and identify
various classical and quantum phases. The frustration is provided by
periodically arranged $0$- and $\pi$- Josephson junctions. In the frustrated
regime the macroscopic phases are composed of different patterns of
vortex/antivortex penetrating each basic element of the Kagome lattice, i.e., a
superconducting triangle interrupted by three Josephson junctions. We obtain
that numerous topological constraints, related to the flux quantization in any
hexagon loop, lead to highly anisotropic and long-range interaction between
well separated vortices (antivortices). Taking into account this interaction
and a possibility of macroscopic "tunneling" between vortex and antivortex in
single superconducting triangles we derive an effective Ising-type spin
Hamiltonian with strongly anisotropic long-range interaction. In the
classically frustrated regime we calculate numerically the
temperature-dependent spatially averaged spins polarization, $\overline{m}(T)$,
characterizing the crossover between the ordered and disordered
vortex/antivortex states. In the coherent quantum regime we analyze the lifting
of the degeneracy of the ground state and the appearance of the highly
entangled states.
