# Computing Wavefunctions of Silicon Donor Qubits with Density Functional Theory

# Computing Wavefunctions of Silicon Donor Qubits with Density Functional Theory

#### Yousif Almullah

Silicon based quantum computing is an attractive approach to large-scale quantum computation due to the significant success of the modern semiconductor fabrication industry. Despite many advances in silicon quantum computing since its inception in 1998, there remains no software for efficiently designing candidate silicon quantum computing devices. Such a development involves modeling the coherence times of qubits and the fidelity of quantum gate operations in a qubit system. The quantum computing group at Oak Ridge National Laboratory propose designing a computational workflow for gauging qubit coherence and gate fidelity for Kane’s proposal of silicon quantum computing. Kane’s model uses electron and nuclear spin states of a P donor atom implanted into a silicon lattice as a qubit, and an oscillating magnetic field to perform quantum gate operations on said qubit. Thus, a computational workflow must consider the electronic structure of a Si:P quantum device, and the wavefunction of the donor electron. This thesis focuses on the donor wavefunction and electronic structure calculations.

The electron density at the phosphorous core gives an approximation to the Fermi contact interaction between nuclear and electron spin states, and is therefore vital to calculating solutions of the time-dependent Hamiltonian representing single-qubit gate operations in Kane’s model. We use the Vienna *ab-initio* Simulation Package (VASP) implementation of density functional theory to compute the valence electron wavefunction of a phosphorous defect in a 1.08 nm silicon nanocluster, and the charge density of this electron. We find the electron density to be 2-4 orders of magnitude below the true electron charge density at the phosphorous nucleus. These data suggest that the pseudo-wavefunctions used by VASP are not accurate enough to inform a silicon quantum computing modeling code.