Implementing a synthetic magnetic vector potential in a 2D superconducting qubit array

Superconducting quantum processors are a compelling platform for analog quantum simulation due to the precision control, fast operation, and site-resolved readout inherent to the hardware. Arrays of coupled superconducting qubits natively emulate the dynamics of interacting particles according to the Bose-Hubbard model. However, many interesting condensed-matter phenomena emerge only in the presence of electromagnetic fields. Here, we emulate the dynamics of charged particles in an electromagnetic field using a superconducting quantum simulator. We realize a broadly adjustable synthetic magnetic vector potential by applying continuous modulation tones to all qubits. We verify that the synthetic vector potential obeys requisite properties of electromagnetism: a spatially-varying vector potential breaks time-reversal symmetry and generates a gauge-invariant synthetic magnetic field, and a temporally-varying vector potential produces a synthetic electric field. We demonstrate that the Hall effect--the transverse deflection of a charged particle propagating in an electromagnetic field--exists in the presence of the synthetic electromagnetic field.