Donor qubits in bulk doped silicon have many competitive advantages for quantum computation in the solid state: not only do they offer a fast way to scalability, but they also show some of the longest coherence times found in any quantum computation proposal. 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 neighbor Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. Third, using the moving-average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of the far-from-equilibrium magnetization dynamics of one species by the orbital excitation of another. We find agreement of our results with a Monte Carlo simulation that handles multiple donor structures and scales optimally with the number of dopants. The simulator can also extract donor structures not captured by our Poisson point process theory. The combined approaches to density optimization in random distributions presented here may be useful for other condensed matter systems as well as applications outside physics.

• Received 23 March 2019
• Revised 6 June 2019

DOI:https://doi.org/10.1103/PhysRevB.100.064201