We use a nonperturbative extended contractor renormalization (ENCORE) method
for engineering quantum devices for the implementation of topologically
protected quantum bits described by an effective quantum dimer model on the
triangular lattice. By tuning the couplings of the device, topological
protection might be achieved if the ratio between effective two-dimer
interactions and flip amplitudes lies in the liquid phase of the phase diagram
of the quantum dimer model. For a proposal based on a quantum Josephson
junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503
(2002)] our results show that optimal operational temperatures below 1 mK can
only be obtained if extra interactions and dimer flips, which are not present
in the standard quantum dimer model and involve three or four dimers, are
included. It is unclear if these extra terms in the quantum dimer Hamiltonian
destroy the liquid phase needed for quantum computation. Minimizing the effects
of multi-dimer terms would require energy scales in the nano-Kelvin regime. An
alternative implementation based on cold atomic or molecular gases loaded into
optical lattices is also discussed, and it is shown that the small energy
scales involved--implying long operational times--make such a device
impractical. Given the many orders of magnitude between bare couplings in
devices, and the topological gap, the realization of topological phases in
quantum devices requires careful engineering and large bare interaction scales.Comment: 12 pages, 10 figure