Quantum Simulation with Semiconductor Quantum Dot Arrays in a Magnetic Field: What is Possible

Semiconductor quantum dot arrays offer a compelling platform for quantum simulation with complex geometries and highly controllable parameters. These arrays provide a way to explore many-body physics and quantum phenomena that was not possible before. In this study, we present a theoretical analysis of quantum dot arrays placed in a magnetic field to manipulate tunnel strengths, imprint phases on the array, and polarize spin. We simulate the system response to increasing magnetic field and investigate the resulting changes in the array behavior. Our simulations extend to larger arrays and various geometries, including squares, loops, and special configurations to engineer the magnetic field response. By understanding how these finite arrays respond to magnetic fields, our results provide insights into the potential for simulating strongly correlated systems and how the behavior will evolve from finite to bulk response (for example how the fractional quantum Hall effect arises). We discuss the systems and phenomena that can be explored using existing experimental setups, showing the possibility of using semiconductor quantum dot arrays for complex quantum simulations in near-future quantum technologies.