Design optimization algorithms and tools for charged-particle optics and trapped ion quantum computing
Keywords: Electrical Engineering.

This thesis studies how to enable computer-aided design for charged particle devices. With the help of computer-aided design, we hope to accelerate innovation in this space by decreasing the time from the conception of an idea to a functioning device. Currently, there is no foundational design tool for charged particle devices. While some researchers have tried to optimize geometries and shapes, their method primarily relied on stochastic searches. Those searches are prohibitively slow for sophisticated geometries and do not scale to complex problems. The lack of a foundational design tool is because the space of charged particle optics poses additional challenges to optimization. These are, amongst others, the nonlinear physical equations describing the physical behavior of charged particle devices and device designs susceptible to minute geometry changes. In this thesis, we discuss these challenges and propose solutions for each. We propose a gradient-based optimization tool that relies on optimization rather than a search and, at its core, computes the gradient highly efficiently. We employ the adjoint variable method (a backpropagation method) to calculate highly accurate gradients of charged particle device systems. This thesis shows the first application of the adjoint variable method for optimizing a charged particle device. We show the vast gain in computational speed achieved by the adjoint variable method, which is more than $30,000$ times faster than currently-used techniques in one of our examples. Specifically, we have implemented four different approaches for our design tool. Out of these, two show promising results --- one based on a finite-element method and one based on a boundary element method. Both design tools were designed, derived, and implemented in-house. We employ the first design tool to optimize electrostatic lenses, improving a lens system's positioning and spot size by six orders of magnitude. Despite this success, this first design tool has several convergence issues, which we address with developing the second design tool. We wrote this design tool in the modern coding framework ``Jax, " which allows for easy integration of this tool into other open-source tools. We show extremely fast convergence for the gradient calculation using this design tool. As gradients are necessary but not sufficient for successfully optimizing charged particle devices, we further developed methods to use the highly-accurate gradients for smooth free-form and more restricted parameter optimizations. We then show how to extend the design tool's problem scope to Helmholtz and Maxwell problems, We also apply our design tool to surface electrode trapped ion quantum computing hardware. The second design tool we describe in this work overcomes all major issues that have impeded the past computer-aided design for charged particle optics. The solutions are very accurate, as the underlying methods (the boundary element method and Verlet-integration) are the gold standards in this field. Moreover, the gradient calculation is accurate to machine precision and converges rapidly, providing stable results even for coarser meshes. It allows for any type of restricted parameter optimization additional to a free-form optimization of the shape. Our research already shows several exciting applications, but many more are possible and can be explored by other researchers