Nanostructure modelling with early fault tolerant quantum computers

Semiconductor nanostructures are central to many developing technologies. Notably, double quantum dots are especially important for semiconductor spin-qubit architectures, quantum sensing applications, and quantum-dot solar cells. Accurate modelling is highly desirable but conventional methods can struggle when dynamics involve more than two interacting electrons. In this work, we present a quantum simulation framework capable of addressing multi-electron double quantum dots. We adopt an efficiently scaling 1^st quantised representation of the system and develop algorithms based on both Trotterisation and qubitisation. Incorporating insights from classical simulations enables us to produce resource estimates that are more realistic than those obtained from theoretical error bounds. Using a standard surface code model with physical noise at 10^-3, our results indicate that the ground-state energy of four electrons in a double quantum dot can be estimated in approximately 24 hours using 226k physical qubits, or an eight-electron system in 3.4 days with 314k qubits (with runtimes falling dramatically when more qubits are available). We anticipate that incorporating very recent advances including dense surface code architectures (Low et al. arXiv:2605.30455) may reduce these costs significantly further. We conclude that early fault tolerant computers may prove to be valuable tools for designing mature-era quantum technologies.