  We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice
with breathing anisotropy (i.e. with weak and strong triangular units),
constructing an improved simplex Resonating Valence Bond (RVB) ansatz by
successive applications (up to three times) of local quantum gates which
implement a filtering operation on the bare nearest-neighbor RVB state. The
resulting Projected Entangled Pair State involves a small number of variational
parameters (only one at each level of application) and preserves full lattice
and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB
provides very good variational energies at strong and even intermediate
breathing anisotropy. We show that it carries $Z_2$ topological order which
does not fade away under the first few applications of the quantum gates,
suggesting that the RVB topological spin liquid becomes a competing ground
state candidate for the kagome antiferromagnet at large breathing anisotropy.
