Kane量子電腦元件的模擬計算

Abstract

In the Kanes proposal of a silicon-based quantum computer architecture, the information are encoded by a array of nuclear spins of 31P as qubits, which are embedded in the isotropically pure 28Si base. Logical gate operations on the qubits are performed by varying external magnetic fields and the electrostatic potential of A-gates,and J-gates, which perturb the electron density to change the strength of hyper ne interaction on individual qubits and exchange interaction between neighbouring qubits.For simplicity, we consider the case that the electric eld is generated by two parallel conducting plates, instead of A and J gate. In this thesis, we focus on simulating the donor electron wave function in the presence of boundaries under the application of an electric field for different device parameters: donor depth, strength of the electric field, and boundary image charges. We calculate the donor electron wave function including the anisotropy of the effective masses in Si, from single-valley to multi-valley using the basis expansion method. We include the boundary image charge effect in our device geometry as was done in M.J.Calderon et al.’s work (M.J.Calderon et al., Phys. Rev. Lett. 96, 096802, 2006), which have calculated the average position of the trial ground state using variational method under the external application of a linear electric eld in different donor depthand estimate the value of their corresponding critical field which can be used to assess the tunnelling time for donor electron ionization. In comparison with M.J.Calderon et al.’s work, we obtain similar results with theirs. Also, we calculate the contact hyperfine coupling energy as function of the strength of electric field in different donor depth. We aim to get physical insight and provide valuable information for the Kane’s quantum computer architecture.