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

Lattice gauge fields via modulation in circuit QED: The bosonic Creutz ladder