Quantum computing promises to revolutionize modern computation. The race to establish a reliable quantum computing system has spurred research over the globe with the goal of establishing a reliable qubit system. One of the more promising candidates are trapped ions. To that end, I have characterized, improved, and designed experiments to be performed in a novel parabolic mirror ion trap. We measured the trap to have a light collection efficiency of 39%, nearly an order of magnitude higher than the light collection of ion traps utilizing standard collection optics. The parabolic mirror also improves the quality of image collected from a trapped ion, but is limited by the micromotion the ion undergoes while at the optical focus. We designed a new trap component to allow radial control over the ion position by moving the RF null, instead of displacing it with DC bias plates. This improved trapping system is a key part of our plan to to remotely entangle an In donor defect in ZnO with a single trapped Yb+ using a 369 nm photon bus. The lifetime of the relevant ionic state is longer than that of the ZnO system by a factor of 6, leading to a greatly decreased temporal overlap in their emitted photons and thus decreased fidelity in the final entangled state if left unattended. This temporal mismatch is a long outstanding challenge when entangling disparate quantum systems, and to address it I performed numerical calculations to design an excitation pulse which can shape the emitted In photon to have an overlap of 0.99 with the Yb+ photon. This leads to a calculated entangled state fidelity of 94% and an entangled state generation rate of 21 kHz with reasonable experimental parameters. Future directions of the parabolic mirror project are the construction of an ellipsoidal mirror trap which is expected to collect light from 95% of the solid angle surrounding a trapped ion. This high light collection will enable investigations into the time dynamics of quantum jumps. These jumps occur when a weakly driven system is continuously measured, and their appearance is entirely random. However, recent work in an artificial superconducting atom suggests that there is a latency period in other transitions which precedes a jump, allowing for these events to be 'caught'. We endeavor to confirm this behavior in a trapped ion, confirming the discovery for a real atomic system.

Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trapped-ion quantum computation by J.I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation are also discussed.

Quantum logic gates are the crucial information-processing operation of quantumcomputers. Two crucial performance metrics for logic gates are their precision andspeed. Quantum processors based on trapped ions have always been the touchstonefor gate precision, but have suffered from slow speed relative to other quantum logicplatforms such as solid state systems. This thesis shows that it is possible to acceleratethe logic "clock speed" from kHz to MHz speeds, whilst maintaining a precision of99.8%. This is almost as high as the world record for conventional trapped-ion gates,but more than 20 times faster. It also demonstrates entanglement generation in atime (480ns) shorter than the natural timescale of the ions' motion in the trap, whichstarts to probe an interesting new regime of ion trap physics. In separate experiments, some of the first "mixed-species" quantum logic gates areperformed, both between two different elements, and between different isotopes.The mixed-isotope gate is used to make the first test of the quantum-mechanical Bellinequality between two different species of isolated atoms.

Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The recognition that the collective behavior of the whole system cannot be simply inferred from an understanding of the behavior of the individual components has led to the development of numerous sophisticated new computational and modeling tools with applications to a wide range of scientific, engineering, and societal phenomena. Computational Complexity: Theory, Techniques and Applications presents a detailed and integrated view of the theoretical basis, computational methods, and state-of-the-art approaches to investigating and modeling of inherently difficult problems whose solution requires extensive resources approaching the practical limits of present-day computer systems. This comprehensive and authoritative reference examines key components of computational complexity, including cellular automata, graph theory, data mining, granular computing, soft computing, wavelets, and more.

The development of scalable microfabricated ion traps with multiple segments for the realization of quantum computing is a challenging task in quantum information science. The research on the design, development, fabrication, and operation of the first European micro-trap is shown in this thesis. This chip-based micro-trap is an outstanding candidate towards experiments for a future quantum processor with trapped single ions. In the experiments coherent quantum state manipulation is demonstrated, and sideband cooling to the motional ground state is realized. The heating rate is determined and the applicability for quantum computation is proven. Furthermore planar trap designs are investigated - a planar microparticle trap was built and operated. A linear microfabricated planar trap was operated, showing the proof of concept of a novel designed and fabricated Y-shaped planar trap.

This volume is a collection of papers from the fourth meeting of the International Symposium on Mesoscopic Superconductivity and Spintronics held at NTT Atsugi, Japan. Research in these fields has advanced a great deal since the previous meeting, largely because these fields have drawn much attention from the viewpoint of new quantum phenomena and quantum information technology. Mesoscopic superconductivity has been developed in new fields, such as a ferromagnet/superconductor junction, the proximity effect in unconventional superconductors, macroscopic quantum tunneling in high-Tc superconductors, quantum modulation of superconducting junctions and superconducting quantum bits. The book also covers transport and spins in nano-scale semiconductor structures such as quantum dots and wires, quantum interference and coherence and order in exotic materials, and some papers on quantum algorithm. This book adequately provides an overview of recent progress in mesoscopic superconductivity.