Quantum computation and simulation is an emerging disruptive technology. Only first suggested by visionaries in the 1980s, in the last 30 years, small quantum computers have become a reality. Using and manipulating the quantum states of trapped atomic ions, simple programs have been run, which if scaled-up, would already give their human users immense advantages in the fields of natural simulations, search and cryptography. Trapped atomic ions have provided the highest fidelity quantum computations and simulations to date. In order to scale-up the use of these systems, several two dimensional (2D) arrays of planar-electrode ion traps were designed, simulated, and tested. The 2D arrays presented here have electronic addressability built into them. By addressable, it is meant that the control of which ion in the trap array participates in any given operation is explicit. A method to address interactions between nearest neighbors in the 2D array using an adjustable radio-frequency voltage is demonstrated by loading calcium ions into the traps and manipulating them. The theory of operation, the design methodology and the method of fabrication of the ion trap arrays is also given.

Ions trapped in Paul traps provide a system which has been shown to exhibit most of the properties required to implement quantum information processing. In particular, a two-dimensional array of ions has been shown to be a candidate for the implementation of quantum simulations. Microfabricated surface geometries provide a widely used technology with which to create structures capable of trapping the required two-dimensional array of ions. To provide a system which can utilise the properties of trapped ions a greater understanding of the surface geometries which can trap ions in two-dimensional arrays would be advantageous, and allow quantum simulators to be fabricated and tested. In this thesis I will present the design, set-up and implementation of an experimental apparatus which can be used to trap ions in a variety of different traps. Particular focus will be put on the ability to apply radio-frequency voltages to these traps via helical resonators with high quality factors. A detailed design guide will be presented for the construction and operation of such a device at a desired resonant frequency whilst maximising the quality factor for a set of experimental constraints. Devices of this nature will provide greater filtering of noise on the rf voltages used to create the electric field which traps the ions which could lead to reduced heating in trapped ions. The ability to apply higher voltages with these devices could also provide deeper traps, longer ion lifetimes and more efficient cooling of trapped ions. In order to efficiently cool trapped ions certain transitions must be known to a required accuracy. In this thesis the 2S1/2 → 2P1/2 Doppler cooling and 2D3/2 → 2D[3/2]1/2 repumping transition wavelengths are presented with a greater accuracy then previous work. These transitions are given for the 170, 171, 172, 174 and 176 isotopes of Yb+. Two-dimensional arrays of ions trapped above a microfabricated surface geometry provide a technology which could enable quantum simulations to be performed allowing solutions to problems currently unobtainable with classical simulation. However, the spin-spin interactions used in the simulations between neighbouring ions are required to occur on a faster time-scale than any decoherence in the system. The time-scales of both the ion-ion interactions and decoherence are determined by the properties of the electric field formed by the surface geometry. This thesis will show how geometry variables can be used to optimise the ratio between the decoherence time and the interaction time whilst simultaneously maximising the homogeneity of the array properties. In particular, it will be shown how the edges of the geometry can be varied to provide the maximum homogeneity in the array and how the radii and separation of polygons comprising the surface geometry vary as a function of array size for optimised arrays. Estimates of the power dissipation in these geometries will be given based on a simple microfabrication.

Systems of trapped ions and systems of ultracold Rydberg atoms are used at the forefront of quantum physics research and they make strong contenders as platforms for quantum technologies. Trapped Rydberg ions are a new hybrid technology envisaged to have both the exquisite control of trapped ion systems and the strong interactions of Rydberg atoms. In this work a single trapped Rydberg ion is experimentally investigated. A trapped strontium ion is excited to Rydberg states using two ultraviolet lasers. Effects of the strong trapping electric fields on the highly-sensitive Rydberg ion are studied. After mitigating unwanted trap effects, the ion is coherently excited to Rydberg states and a quantum gate is demonstrated. This thesis lays much of the experimental groundwork for research using this novel system.

The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include: Key topics include: - Quantum error correction codes (QECCs), including stabilizer codes, Calderbank-Shor-Steane (CSS) codes, quantum low-density parity-check (LDPC) codes, entanglement-assisted QECCs, topological codes, and surface codes - Quantum information theory, and quantum key distribution (QKD) - Fault-tolerant information processing and fault-tolerant quantum error correction, together with a chapter on quantum machine learning. Both quantum circuits- and measurement-based quantum computational models are described - The next part of the book is spent investigating physical realizations of quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps - In-depth analysis of the design and realization of a quantum information processing and quantum error correction circuits This fully up-to-date new edition will be of use to engineers, computer scientists, optical engineers, physicists and mathematicians. - A self-contained introduction to quantum information processing, and quantum error correction - Integrates quantum information processing, quantum computing, and quantum error correction - Describes the latest trends in the quantum information processing, quantum error correction and quantum computing - Presents the basic concepts of quantum mechanics - In-depth presentation of the design and realization of a quantum information processing and quantum error correction circuit

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.

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 book constitutes the refereed proceedings of the 9th International Conference on Reversible Computation, RC 2017, held in Kolkata, India, in July 2017. The 13 full and 5 short papers included in this volume together with one invited paper were carefully reviewed and selected from 47 submissions. The papers are organized in the following topical sections: foundations; reversible circuit synthesis; reversible circuit optimization; testing and fault tolerance; and quantum circuits.