Uniqueness of Hubbard parameter identification from charge stability diagrams

Determine whether the collection of charge stability diagrams measured for nearest-neighbor pairs of semiconductor quantum dots over varying local chemical potentials uniquely determines the site-dependent parameters of the extended Hubbard model—specifically the hopping amplitudes t_ij, on-site energies ε_i, inter-site Coulomb repulsions V_ij, and on-site Coulomb repulsions U_i—thereby establishing the injectivity of the mapping from aggregated stability-diagram data to the full Hamiltonian parameter set.

Background

The paper introduces a convolutional neural network approach to infer site-specific disorder in the extended Hubbard model describing semiconductor quantum dot qubit arrays. The inputs are experimentally accessible charge stability diagrams obtained from nearest-neighbor dot pairs under varying gate voltages (chemical potentials), and the outputs are the deviations in all Hubbard parameters across sites.

While the method empirically recovers the parameters with high accuracy across multiple scenarios, the authors note that a formal guarantee of uniqueness or invertibility of the mapping from aggregated charge stability diagrams to Hubbard parameters has not been established. In particular, there is no proven analogue of an inverse scattering theorem in this context, raising the foundational question of whether such data determine the parameters uniquely in general.