Critical challenges in donor based quantum computation

Building a scalable quantum computer is one of the most interesting and difficult problems facing the world of physics today. The requirements for building such a machine are stringent and a number of critical challenges must be overcome before it is achieved. This thesis represents an effort to mitigate some of the challenges for the donor based Kane quantum computer and its derivatives.At the Centre of Quantum Communication and Computation, UNSW, we use scanning tunnelling microscope (STM) lithography to place individual phosphorus donors into the lattice of isotopically pure 28Si. For phosphorus in silicon (Si:P) based quantum computation, a complete understanding of tunnelling rates between planar, STM patterned regions is crucial to control and operate single electron transistors and charge sensors. Furthermore, tunnelling rates between qubits is vitally important in information flow through a quantum computer. In this thesis, systematic sets of atomically precise tunnel gaps are fabricated and characterised. From this we extract the dependence of tunnel rates and potential barriers as a function of gap dimensions and discuss suitable modelling methods for the simulating tunnelling devices and qubits.A fundamental component of STM patterned Si:P device architecture is the two dimensional, planar, phosphorus doped delta-layer. We characterise the energy quantisation of delta layers by two separate experimental techniques, which, through an international collaboration, is compared to atomistic tight-binding models. Schottky barrier spectroscopy is used to measure the density of states of delta layers across a range of doping densities, while STM spectroscopy is used to investigate the variation and disorder of the delta-layer.To assist in qubit coherence times, a new dynamical decoupling scheme to preserve quantum states during quantum computation is investigated. Combining ideas from separate dynamical decoupling sequences a dramatic increase in qubit coherence times is achieved, in a way that is robust to common experimental errors.Finally, an improved quantum algorithm is presented for the dihedral hidden subgroup problem. By augmenting a subexponential time algorithm with a quantum search, I show an improvement of five orders of magnitude for the common 256 bit key size in lattice based cryptography over previously described algorithms, and optimise the size of the quantum search in the new algorithm for best performance