  We describe a lattice of asymmetrical qubit pairs in one or two dimensions,
with couplings arranged so that the motion of single-qubit excited states
mimics the behavior of charged lattice bosons hopping in a magnetic field. We
show in particular that one can choose the parameters of the many-body circuit
to reach a regime where the complex hopping phase between any two elements can
be tuned to any value by simply adjusting the relative phases of two applied
oscillating voltage signals. We also propose a specific realization of our
model using coupled three junction flux qubits, in which one can reach the
strongly interacting bosonic quantum Hall limit where one will find anyonic
excitations. The circuits could be used for topological quantum computation.
