The impact of donor incorporation statistics on analog quantum simulations of Hubbard physics in near-atomic precision donor arrays

Atomic precision advanced manufacturing (APAM) is a promising approach for analog quantum simulation of strongly correlated systems. APAM relies on scanning tunneling microscope lithography to place single P donors precisely in Si. Assessing the impact of experimentally demonstrated stochastic donor incorporation on device performance is vital to understanding the limits of analog quantum simulation. Using a nonequilibrium Green’s function formalism, we simulate transport characteristics of Hubbard models based-on P donors in Si, and the effects of probabilistic donor incorporation on these transport characteristics. Using our model, we find limits on the Hamiltonians one can target without losing prominent physical features of the model to missing donors.