Realizing a parametrically coupled lattice of superconducting qubits for quantum simulation with a synthetic magnetic field*

Advances in quantum computing hardware have made possible the burgeoning field of quantum simulation of condensed matter systems. Arrays of superconducting qubits, in particular, offer native emulation of lattice physics together with a high degree of tunability. Emulation of magnetic fields, however, is a challenge in this platform, yet magnetic fields are a central ingredient in many models of interest. Here, we introduce a scheme to emulate the dynamics of charge carriers through a magnetic field by parametrically driving hopping of microwave photons between transmon qubits. Implementing our scheme in a 4-by-4 array of qubits, we emulate arbitrary magnetic fields with uniform and disordered field profiles. We verify key signatures of the presence of a synthetic magnetic field, and we discuss challenges to implementing the scheme on real-world hardware.