Quantum Algorithms, Architecture, and Error Correction

TL;DR

This paper explores quantum algorithms, architectures, and error correction techniques, highlighting recent advances in quantum optimization, simulation, logical operations, and error correction software to enable scalable quantum computing.

Contribution

It introduces new algorithms, simulation methods, and procedures for quantum error correction, advancing the development of reliable, large-scale quantum computers.

Findings

Improved runtime performance for topological stabilizer codes.

Analysis of QAOA performance on Max Cut problem.

Development of software for quantum error correction evaluation.

Abstract

Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of optimization, material science, chemistry, and biology. Thus, the realization of large-scale, reliable quantum-computers will likely have a significant impact on the world. For this reason, the focus of this dissertation is on the development of quantum-computing applications and robust, scalable quantum-architectures. I begin by presenting an overview of the language of quantum computation. I then, in joint work with Ojas Parekh, analyze the performance of the quantum approximate optimization algorithm (QAOA) on a graph problem called Max Cut. Next, I present a new stabilizer simulation algorithm that gives improved runtime performance for topological stabilizer codes. After that, in joint work with Andrew Landahl, I present a new set of procedures for performing logical operations called "color-code lattice-surgery." Finally, I describe a software package I developed for studying, developing, and evaluating quantum error-correcting codes under realistic noise.