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.

Over the past 15 years ion traps have demonstrated all the building blocks required of a quantum computer. Despite this success, trapping ions remains a challenging task, with the requirement for extensive laser systems and vacuum systems to perform operations on only a handful of qubits. To scale these proof of principle experiments into something that can outperform a classical computer requires an advancement in the trap technologies that will allow multiple trapping zones, junctions and utilize scalable fabrication technologies. I will discuss the construction of an ion trapping experiment, focussing on my work towards the laser stabilization and ion trap design but also covering the experimental setup as a whole. The vacuum system that I designed allows the mounting and testing of a variety of ion trap chips, with versatile optical access and a fast turn around time. I will also present the design and fabrication of a microfabricated Y junction and a 2- dimensional ion trap lattice. I achieve a suppression of barrier height and small variation of secular frequency through the Y junction, aiding to the junctions applicability to adiabatic shuttling operations. I also report the design and fabrication of a 2-D ion trap lattice. Such structures have been proposed as a means to implement quantum simulators and to my knowledge is the first microfabricated lattice trap. Electrical testing of the trap structures was undertaken to investigate the breakdown voltage of microfabricated structures with both static and radio frequency voltages. The results from these tests negate the concern over reduced rf voltage breakdown and in fact demonstrates breakdown voltages significantly above that typically required for ion trapping. This may allow ion traps to be designed to operate with higher voltages and greater ion-electrode separations, reducing anomalous heating. Lastly I present my work towards the implementation of magnetic fields gradients and microwaves on chip. This may allow coupling of the ions internal state to its motion using microwaves, thus reducing the requirements for the use of laser systems.

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.

Universal, fault-tolerant quantum computing would require millions of physical qubits to practically implement most proposed algorithms, a target currently out of reach of experimental capability. In the near term, noisy systems on the order of tens of qubits can employ quantum simulation of particular Hamiltonians to surpass classical computational abilities and solve interesting problems. In particular, one-dimensional (1D) ion chains in radiofrequency (RF) traps have seen remarkable success in simulating 1D quantum spin systems. A comparable ability to manipulate two-dimensional (2D) ion crystals in RF traps would significantly expand the class of systems accessible to quantum simulation. Notably, 2D ion arrays are conducive to studies of many-body systems such as geometrically frustrated lattices, topological materials, and spin-liquid states.In this thesis, I present advances toward the goal of creating programmable, "radial-2D" arrays of trapped 171Yb+ ions for quantum simulation. Qubits are embedded within two hyperfine electronic energy levels, cooled to their motional ground state, and measured via spin-dependent fluorescence. A precisely controlled entangling mechanism allows for the creation of a wide variety of spin models, including Ising or Heisenberg interactions. We present an experimental study which establishes radial-2D crystals of 171Yb+ ions as a robust platform for quantum simulation, through characterization of ion positions, structural phases, normal mode frequencies, and effects from RF heating. We also design and experimentally demonstrate a new open-endcap, blade-style RF trap which can confine and resolve large numbers of ions in the radial-2D crystal phase. Finally, we examine other challenges faced by trapped ion systems: optimally cooling to the motional ground state, accurately determining ion temperature, and measuring susceptibility to the presence of ionizing radiation.

Trapped ions are currently one of the most promising architectures for realising the quantum information processor. The long lived internal states are ideal for representing qubit states and, through controlled interactions with electromagnetic radiation, ions can be manipulated to execute coherent logic operations. In this thesis an experiment capable of trapping Yb+ ions, including 171Yb+, is presented. Since ion energy can limit the coherence of qubit manipulations, characterisation of an ion trap heating rate is vital. Using a trapped 174Yb+ ion a heating rate consistent with previous measurements of other ion species in similar ion traps is obtained. This result shows abnormal heating of Yb+ does not occur, further solidifying the suitability of this species for quantum information processing. Efficient creation, and cooling of trapped ions requires exact wavelengths for the ionising, cooling and repump transitions. A simple technique to measure the 1S0 ↔ 1P1 transition wavelengths, required for isotope selective photoionisation of neutral Yb, is developed. Using the technique new wavelengths, accurate to 60 MHz, are obtained and differ from previously published results by 660 MHz. Through a simple modification the technique can also predict Doppler shifted transition frequencies, which may be required in non-perpendicular atom-laser interactions. Using trapped ions, the 2S1=2 ↔ 2P1/2 Doppler cooling and 2D3/2 ↔ 2D[3/2]1/2 repump transitions are also measured to a greater accuracy than previously reported. Many experiments require wavelengths which can only be obtained using complex expensive laser systems. To remedy this a simple cost effective laser is developed to enable laser diodes to be operated at sub zero temperatures, extending the range of obtainable wavelengths. Additional diode modulation capabilities allow for the manipulation of atoms and ions with hyperfine structures. The laser is shown to be suitable for manipulating Yb+ ions by cooling a diode from 372 nm to 369 nm and simultaneously generating 2.1 GHz frequency sidebands. Coherent manipulation such as arbitrary qubit rotations, motional coupling and ground state cooling, are required for trapped ion quantum computing. Two photon stimulated Raman transitions are identified as a suitable technique to implement all of these requirements and an investigation into implementing this technique with 171Yb+ is conducted. The possibility of exciting a Raman transition via either a dipole or quadrupole transitions in 171Yb+ is analysed, with dipole transitions preferred because quadrupole transitions are found to be too demanding experimentally. An inexpensive setup, utilising a dipole transition, is designed and tested. Although currently limited the setup shows potential to be an inexpensive, high fidelity method of exciting a Raman transition.

In this late-start Tier I Seniors Council sponsored LDRD, we have designed, simulated, microfabricated, packaged, and tested ion traps to extend the current quantum simulation capabilities of macro-ion traps to tens of ions in one and two dimensions in monolithically microfabricated micrometer-scaled MEMS-based ion traps. Such traps are being microfabricated and packaged at Sandia's MESA facility in a unique tungsten MEMS process that has already made arrays of millions of micron-sized cylindrical ion traps for mass spectroscopy applications. We define and discuss the motivation for quantum simulation using the trapping of ions, show the results of efforts in designing, simulating, and microfabricating W based MEMS ion traps at Sandia's MESA facility, and describe is some detail our development of a custom based ion trap chip packaging technology that enables the implementation of these devices in quantum physics experiments.

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.