This paper presents a method to implement a synthetic magnetic vector potential in a 2D array of superconducting qubits, enabling the emulation of charged particles in an electromagnetic field. The authors use continuous modulation tones to apply a synthetic magnetic vector potential, which breaks time-reversal symmetry and generates a gauge-invariant synthetic magnetic field. They verify that the synthetic vector potential obeys the properties of electromagnetism, including the breaking of time-reversal symmetry and the generation of a synthetic electric field. The Hall effect, where a charged particle is deflected transversely in an electromagnetic field, is demonstrated in the presence of the synthetic electromagnetic field. The experiment involves 16 transmon qubits arranged in a 4x4 grid, with nearest-neighbor capacitive coupling. The synthetic vector potential is realized by parametrically modulating the qubits, creating complex hopping rates and Peierls phases. The results show that the synthetic magnetic field exhibits gauge invariance and that the Hall effect is observed when both synthetic electric and magnetic fields are applied. This work provides a platform for simulating various condensed-matter phenomena, including the quantum Hall effect and Majorana excitations, using a superconducting quantum simulator.This paper presents a method to implement a synthetic magnetic vector potential in a 2D array of superconducting qubits, enabling the emulation of charged particles in an electromagnetic field. The authors use continuous modulation tones to apply a synthetic magnetic vector potential, which breaks time-reversal symmetry and generates a gauge-invariant synthetic magnetic field. They verify that the synthetic vector potential obeys the properties of electromagnetism, including the breaking of time-reversal symmetry and the generation of a synthetic electric field. The Hall effect, where a charged particle is deflected transversely in an electromagnetic field, is demonstrated in the presence of the synthetic electromagnetic field. The experiment involves 16 transmon qubits arranged in a 4x4 grid, with nearest-neighbor capacitive coupling. The synthetic vector potential is realized by parametrically modulating the qubits, creating complex hopping rates and Peierls phases. The results show that the synthetic magnetic field exhibits gauge invariance and that the Hall effect is observed when both synthetic electric and magnetic fields are applied. This work provides a platform for simulating various condensed-matter phenomena, including the quantum Hall effect and Majorana excitations, using a superconducting quantum simulator.