  In this work we propose two protocols to make an effective gauge potential
for microwave photons in circuit QED. The schemes consist of coupled transmons
whose flux are harmonically modulated in time. We investigate the effect of
various types of capacitive and inductive couplings, and the role of the fixed
phase offset of each site on the complex coupling rate between coupled qubits.
These configurations can be directly realised in a superconducting circuit and
is easily extendable to a scalable lattice. Due to the intrinsic non-linearity
of the transmon qubits such lattices would be an ideal platform for simulating
Bose-Hubbard Hamiltonians with non-trivial gauge fields.
