Scalable Trapped Ion Quantum Computing

Abstract

Trapped ions are a promising platform for universal quantum computing, but are currently limited in their scalability to tens of qubits. A key limiting factor to scalability is the difficulty in performing sufficiently fast high-fidelity entangling gates in architectures with large numbers of qubits. Proposals to circumvent this limitation have focused on architectures that involve physically shuttling of ions between separate traps. Entangling gates using a sequence of ultrafast π-pulses, often referred to as "fast gates", are a promising approach to achieving scalable trapped ion quantum computing. This thesis begins with a brief introduction to quantum computing and an overview of current progress towards scalable quantum computing on several prominent platforms. We then give a specific overview of trapped ion quantum computing and develop in detail the models of light and matter interactions that underpin trapped ion quantum computing. We investigate the use of various "fast gate" schemes in linear Paul traps containing a large number of ions, architectures based on the trapping of ions in individual 'microtraps', and multi-dimensional extensions to these architectures. The scalability of these architectures to larger numbers of qubits is examined and the impact of potential sources of experimental error is explored. We find that "fast gates" using a series of ultrafast π-pulses are capable of implementing two-qubit entangling gates above fault-tolerant thresholds in scalable architectures. These can achieve gate times that are substantially shorter than the trapping period significantly faster than current entangling gate schemes. The technical requirements for achieving these short gate times and fidelities are relatively modest. The most significant limitation is the fidelity of the individual π-pulses. We further find that "fast gates" offer faster entangling operations between ions in separate traps, eliminating the need to design electrode structures that allow for the comparatively slower shuttling process. We examine the effects of the oscillating electric potential ("micromotion") used to trap the ions, finding a significant detrimental impact if not considered in the design process. Somewhat intuitively, we find micromotion has a beneficial effect on gates designed to include its effects, substantially reducing the technical requirements to implement shorter gate times. We find that "fast gates" are well suited to multi-dimensional architectures, which provide a reduction in the number of two-qubit entangling operations required to implement some algorithms. Finally, we conclude that "fast gates" implemented on a scalable architecture offers a realistic pathway to implementing useful algorithms that are intractable using classical computers.