Simulation of Si:P spin-based quantum computer architecture

We present a systematic and realistic simulation for single and double phosphorous donors in a silicon-based quantum computer design. A two-valley equation is developed to describe the ground state of phosphorous donors in a strained silicon quantum well (QW), with the central cell effect treated by a model impurity potential. The valley splitting of the donor ground state as a function of QW width or donor position is calculated and a comparison with the valley splitting of the lowest QW states is presented. Oscillation of the valley splitting is observed as the QW width or donor position is varied at atomic scale. We find that the increase of quantum well confinement leads to shrinking charge distribution in all three dimensions. Using an unrestricted Hartree-Fock method with generalized valence bond (GVB) single-particle wave functions, we are able to solve the two-electron Schrödinger equation with quantum well confinement and realistic gate potentials. The lowest singlet and triplet energies and their charge distributions for a neighboring donor pair in the quantum computer (QC) architecture are obtained at different gate voltages. The effects of QW width, gate voltages, donor separation, and donor position shift are calculated and analyzed. The gate tunability and gate fidelity are defined and evaluated, for a typical QC design. Estimates are obtained for the duration of spin-half-swap gate operation and the required accuracy in voltage control. A strong exchange oscillation is observed as both donors are shifted along [001] axis but with their separation unchanged. Applying a gate potential tends to suppress the oscillation. The exchange oscillation as a function of donor separation along [100] axis is found to be completely suppressed as the donor separation is decreased. The simulation presented in this paper is of importance to the practical design of an exchange-based silicon quantum computer.