PhD Proposal: Qunity and COGNAC: Finding the Right Abstractions for Quantum Programming

Quantum computing holds the potential to transform fields such as material science and cryptography, yet the development of effective programming tools remains a key challenge. This proposal explores the integration of interdisciplinary techniques to enhance quantum programming languages, focusing on Qunity, a novel language designed to unify classical and quantum paradigms. I propose extending Qunity with features like higher-order functions, recursion, and polymorphism. With lower-level compiler optimizations such as COGNAC's noise-aware circuit optimization, the research aims to address existing limitations and improve efficiency and scalability. Drawing from ideas outside of programming languages, the work seeks to provide new insights into the design and compilation of quantum programs, improving accessibility and performance in quantum software development. Implementing the HHL algorithm will demonstrate Qunity's capability to handle bounded-error quantum subroutines, offering a promising path toward robust quantum programming tools.