Randomly-doped silicon has many competitive advantages for quantum computation; not only is it fast to fabricate but it could naturally contain high numbers of qubits and logic gates as a function of doping densities. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations of the dopants necessary for them to form exchange interaction mediated entangling gates. Second, using nearest neighbour Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. We find agreement of our results with a Monte Carlo simulation, for which we present the algorithms, which handles multiple donor structures and scales optimally with the number of dopants and use it to extract donor structures not captured by our Poisson point process theory. Third, using the moving average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of one species by the orbital excitation of another. These combined approaches to density optimization in random distributions may be useful for other condensed matter systems as well as applications outside physics.

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