This paper presents a method to simulate electromagnetic fields using a 2D array of superconducting qubits. The researchers demonstrate the ability to generate a synthetic magnetic vector potential by applying continuous modulation tones to all qubits. They verify that this synthetic vector potential obeys the properties of electromagnetism, including generating a gauge-invariant synthetic magnetic field and a synthetic electric field when the vector potential varies in time. The team observes the Hall effect, where a charged particle is deflected transversely in the presence of both synthetic electric and magnetic fields. The study uses a 16-qubit superconducting processor arranged in a 4x4 grid. The qubits are coupled through fixed mutual capacitance, and the synthetic vector potential is created by modulating the qubits with control tones. The phases of these modulation tones form the synthetic vector potential, which can be adjusted to break time-reversal or spatial-inversion symmetry. The researchers demonstrate that the synthetic vector potential can be used to emulate the dynamics of charged particles in electromagnetic fields, including Aharonov-Bohm interference, Bloch oscillations, and the Hall effect. The study shows that the synthetic magnetic vector potential can be used to emulate a wide range of electromagnetic field strengths and profiles, including spatially nonuniform and time-varying fields. The results confirm that the synthetic vector potential behaves consistently with two of Maxwell's equations: Gauss's law for magnetism and Faraday's law. The team also demonstrates that the synthetic magnetic field can be used to study various quantum phenomena, including the integer and fractional quantum Hall effects. The work provides a new platform for creating artificial matter in high magnetic fields, enabling the study of complex magnetic environments. The methods described can be used to simulate a variety of condensed-matter phenomena, including those that are difficult to study in natural materials. The study highlights the potential of superconducting quantum processors as a powerful tool for analog quantum simulation.This paper presents a method to simulate electromagnetic fields using a 2D array of superconducting qubits. The researchers demonstrate the ability to generate a synthetic magnetic vector potential by applying continuous modulation tones to all qubits. They verify that this synthetic vector potential obeys the properties of electromagnetism, including generating a gauge-invariant synthetic magnetic field and a synthetic electric field when the vector potential varies in time. The team observes the Hall effect, where a charged particle is deflected transversely in the presence of both synthetic electric and magnetic fields. The study uses a 16-qubit superconducting processor arranged in a 4x4 grid. The qubits are coupled through fixed mutual capacitance, and the synthetic vector potential is created by modulating the qubits with control tones. The phases of these modulation tones form the synthetic vector potential, which can be adjusted to break time-reversal or spatial-inversion symmetry. The researchers demonstrate that the synthetic vector potential can be used to emulate the dynamics of charged particles in electromagnetic fields, including Aharonov-Bohm interference, Bloch oscillations, and the Hall effect. The study shows that the synthetic magnetic vector potential can be used to emulate a wide range of electromagnetic field strengths and profiles, including spatially nonuniform and time-varying fields. The results confirm that the synthetic vector potential behaves consistently with two of Maxwell's equations: Gauss's law for magnetism and Faraday's law. The team also demonstrates that the synthetic magnetic field can be used to study various quantum phenomena, including the integer and fractional quantum Hall effects. The work provides a new platform for creating artificial matter in high magnetic fields, enabling the study of complex magnetic environments. The methods described can be used to simulate a variety of condensed-matter phenomena, including those that are difficult to study in natural materials. The study highlights the potential of superconducting quantum processors as a powerful tool for analog quantum simulation.