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

Superconducting quantum processors are a compelling platform for analogue 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 the required 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.