Analog Quantum Simulators: Magnetic Field Effects in Semiconductor Quantum Dot Arrays

Semiconductor quantum dot arrays provide a powerful platform for analog quantum simulation, which can explore strongly correlated electron systems with atomic precision and highly tunable parameters. These systems naturally realize the Fermi–Hubbard model and can capture complex many-body phenomena with greater efficiency and fewer resources than digital quantum processors, allowing access to phenomena such as quantum magnetism, superconductivity, and quantum Hall physics that are otherwise classically intractable. In this work, we present theoretical studies of semiconductor quantum dot arrays subjected to external magnetic fields, revealing the emergence of edge and bulk states across various geometries and field strengths. Our simulations capture edge states and circulating edge currents, which is how the integer and fractional quantum Hall effects manifest in finite systems. As the array size increases, the system exhibits behavior that approaches the bulk limit. These results provide theoretical benchmarks for ongoing and near-term experiments and highlight the potential of semiconductor quantum dot arrays as versatile quantum simulators for studying correlated electron phenomena.