Quantum Computation with Electron Spins of Phosphorous Donors in Silicon

The discovery of efficient quantum algorithms a decade ago has shown that a quantum computer encoding and processing information quantum mechanically, can solve important problems intractable with conventional computers. The invention of quantum error correction principle, makes quantum computation possibly fault-tolerant against the decoherence of information carriers. Thereafter, intensive research activities have been made toward the implementation of quantum computation with various realistic quantum systems. Among them, the most attractive implementation proposals are using silicon-based materials, which have the advantage of borrowing the existing ingenuity and resources accumulated during the development of modern microelectronics. In this dissertation we investigate several theoretical aspects of a siliconbased quantum computer in which qubits are represented by the spins of electrons bound to phosphorous donors in silicon. Encoding each qubit in terms of three neighboring donor electron spins, we can realize universal quantum gate operations with only the Heisenberg exchange coupling JS1 ·S2 between neighboring donors. Therefore, studying the exchange coupling for a phosphorous donor pair in silicon is of central importance for providing the experimentalists with qualitative insights and quantitative guidance for building such a silicon quantum computer. After giving some general considerations on the quantum computer architecture, we develop the necessary theoretical tools. A multi-valley effective mass equation is derived and discussed, to handle impurities in a multi-valley semiconductor. Then we apply it to solve a single Si:P donor embedded in our quantum computer architecture. We show that the width of the silicon quantum well can significantly influence the energy splitting and charge distributions of the ground state. Oscillation of level splitting is observed as the quantum well width or donor position is varied at atomic scale. Elementary gate operations for 3-donor-spin qubits involve a neighboring pair of donors at each step. The exchange coupling in Heisenberg model