School of Physics

This thesis investigates several broad areas related to the eﬀective implementation of quantum information processing, from large scale quantum algorithms and error correction, through to system identiﬁcation and characterization techniques, eﬃcient designs for quantum computing architectures and the design of small devices which utilize quantum eﬀects. The discussion begins with the introduction of a quantum circuit appropriate for implementing Shor’s factoring algorithm on Linear Nearest Neighbor qubit arrays such as the Kane phosphorus in silicon system. Detailed numerical sim- ulations are then presented, demonstrating the sensitivity of the circuit under coherent quantum errors. The concepts of Quantum Error Correction and Fault-tolerant computation are reviewed with original work carried out to show the relative robustness and practicality of Fault-tolerant computation for logical state preparation. Methods of intrinsic system identiﬁcation and characterization are proposed. Protocols for characterizing both the conﬁnement of a multi-level system to the qubit subspace and the Hamiltonian dynamics governing two-qubit interactions are presented as well as a brief review of characterization techniques already developed for single qubit dynamics. (For complete abstract open document)

This thesis examines methods for obtaining the full complex wave-field from measured probability intensities in microscopy experiments, otherwise known as the phase problem. We present a new theoretical framework for solving the phase problem. From this, previously intractable problems may be solved via direct methods. In addition, we present a method for greatly increasing the potential output of single particle diffraction measurements in free-electron laser science (FELS) experiments. This method extracts many single particle diffraction measurements from a single many particle diffraction measurement. We investigate the feasibility for performing coherent diffractive imaging (CDI) in the scanning transmission electron microscopy (STEM) geometry using standard methods. Despite some success in ideal cases, we find that the inversions (from the measured diffraction intensities to the complex wave-field) are very sensitive to imperfections in the data. Consequently we investigate the degree to which various sources of error, such as detector noise and spatial incoherence, affect the convergence properties of the inversions. Difficulties in the application of single-shot CDI in STEM may be overcome by measuring many diffraction patterns from the same sample and combining these data for a ptychographic method. We performed a ptychographic reconstruction of a complex sample transmission function. This was done by combining several diffraction measurements from overlapping regions of a boron-nitride cone. We present the subsequent atomic resolution retrieval and the algorithm used. We develop and implement new holographic algorithm to obtain a high resolution reconstruction of the complex exit surface wave formed by a gnat’s wing. In doing so we derive a new error metric applicable in both holographic and non-linear CDI. It is also found to be a more reliable measure for the fidelity of the retrieval. By extending the previous holographic method to accommodate diffraction data taken in the near-field (or the Fresnel regime) we find that previous restrictions on the illumination and the position of the sample in the beam are greatly reduced. We demonstrate the experimental feasibility of this method by recombining the complex exit surface wave emanating from a microfibre. Here the specimen was illuminated by a plane wave while the diffraction data was taken in a plane centimetres from the object. We show how the requirement for full coherence of the imaging system can be removed by incorporating the partially coherent modes of the imaging probe into the formalism of the holographic method. A new iterative linear algorithm is developed, extending the applicability of the algorithm to higher resolutions and greatly increasing the computational speed of the retrieval. We present a direct single-shot sub-Angström retrieval from the edge structure of a CeO2 nano-particle, using electrons. This retrieval is improved by the inclusion of the entire autocorrelation function of the exit surface wave. Using the new iterative linear algorithm we are able to include a subsequent iteration, correcting for the non-linear contribution to the autocorrelation function by the object. Finally, we use the techniques developed in this thesis to extend the new iterative linear algorithm to include ptychographic data-sets.

School of Physics - Theses

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