The major challenges in trapped-ion quantum computation are to scale up few-ion experiments to many qubits and to improve control techniques so that quantum logic gates can be carried out with higher fidelities. This thesis reports experimental progress in both of these areas. In the early part of the thesis we describe the fabrication of a surface-electrode ion trap, the development of the apparatus and techniques required to operate it and the successful trapping of 40Ca+ ions. Notably we developed methods to control the orientation of the principal axes and to minimise ion micromotion. We propose a repumping scheme that simplifies heating rate measurements for ions with low-lying D levels, and use it to characterise the electric field noise in the trap. Surface-electrode traps are important because they offer a route to dense integration of electronic and optical control elements using existing microfabrication technology. We explore this scaling route by testing a series of three traps that were microfabricated at Sandia National Laboratories. Investigations of micromotion and charging of the surface by laser beams were carried out and improvements to future traps are suggested. Using one of these traps we also investigated anomalous electrical noise from the electrode surfaces and discovered that it can be reduced by cleaning with a pulsed laser. A factor of two de- crease was observed; this represents the first in situ removal of this noise source, an important step towards higher gate fidelities. In the second half of the thesis we describe the design and construction of an experiment for the purpose of replacing laser-driven multi-qubit quantum logic gates with microwave-driven ones. We investigate magnetic-field-independent hyperfine qubits in 43Ca+ as suitable qubits for this scheme. We make a design study of how best to integrate an ion trap with the microwave conductors required to implement the gate and propose a novel integrated resonant structure. The trap was fabricated and ions were successfully loaded. Single-qubit experiments show that the microwave fields above the trap are in excellent agreement with software simulations. There are good prospects for demonstrating a multiqubit gate in the near future. We conclude by discussing the possibilities for larger-scale quantum computation by combining microfabricated traps and microwave control.

Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

This stimulating discussion of a rapidly developing field is divided into two parts. The first features tutorials in textbook style providing self-contained introductions to the various areas relevant to atom chip research. Part II contains research reviews that provide an integrated account of the current state in an active area of research where atom chips are employed, and explore possible routes of future progress. Depending on the subject, the length of the review and the relative weight of the 'review' and 'outlook' parts vary, since the authors include their own personal view and style in their accounts.

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.

Trapped ions are a promising approach to quantum computation. This approach uses a qubit state which is the atomic state and quantum motional state of a trapped ion to encode information, and uses laser-ion interactions to manipulate the qubit state. A major obstacle to the realization of a practical ion trap quantum computer is decoherence. In trapped ion quantum computation experiments, decoherence is dominated by the uncontrolled heating of ion motional states. In this thesis, we present the detailed microfabrication of several series of surface electrode linear Paul traps made from different electrode materials, followed by the ion motional heating experiment results for these traps. We demonstrate that the ion motional heating strongly depends on fabrication process. In particular, we explore how grain size and grain orientation affect the ion motional heating rate. This thesis is divided into two parts. In the first part, we describe the fabrication of gold, silver, aluminum and niobium traps from different processes, which results in various surface morphologies and grain structures. Ion motional heating rate measurements are then conducted both at cryogenic temperatures and at room temperature. We employ a physical model based on the fluctuating patch potential theory to explain the ion heating behavior. We use gold traps to study the temperature and frequency dependence of the ion heating. We use aluminum traps to study the ion heating dependence on the amorphous dielectric layer. And we use silver traps to study the ion heating dependence on the grain structure. These results suggest that excess ion heating could possibly be suppressed by suitable fabrication selection. In the second part, we present the process of using SU8 to fabricate a multilayer surface electrode point Paul trap, which has the advantage of allowing ion height variation within the same trap and enables testing of the distance dependence of ion heating.

Universal quantum computation requires precision control of the dynamics of qubits. Frequently accurate quantum control is impeded by systematic drifts and other errors. Compensating composite pulse sequences are a resource efficient technique for quantum error reduction. This work describes compensating sequences for ion-trap quantum computers. We introduce a Lie-algebraic framework which unifies all known fully-compensating sequences and admits a novel geometric interpretation where sequences are treated as vector paths on a dynamical Lie algebra. Using these techniques, we construct new narrowband sequences with improved error correction and reduced time costs. We use these sequences to achieve laser addressing of single trapped 40Ca+ ions, even if neighboring ions experience significant field intensity. We also use broadband sequences to achieve robust control of 171Yb+ ions even with inhomogeneous microwave fields. Further, we generalize compensating sequences to correct certain multi-qubit interactions. We show that multi-qubit gates may be corrected to arbitrary accuracy if there exists either two non-commuting controls with correlated errors or one error-free control. A practical ion-trap quantum computer must be extendible to many trapped ions. One solution is to employ microfabricated surface-electrode traps, which are well-suited for scalable designs and integrated systems. We describe two novel surface-electrode traps, one with on-chip microwave waveguides for hyperfine 171Yb+ qubit manipulations, and a second trap with an integrated high numerical aperture spherical micromirror for enhanced fluorescence collection.

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.