Program Synthesis for Quantum Applications

Abstract

Quantum computing has the potential to revolutionize various fields by solving problems intractable for classical computers. However, developing efficient quantum programs remains challenging due to the unique constraints of quantum systems, including noise, limited qubit connectivity, and hardware variability. Unlike classical programming, where high-level abstractions and optimized compilers ease development, quantum programming still relies heavily on low-level circuit representations, making manual implementation complex and error-prone. Program syn-thesis, an approach that automatically generates programs satisfying given specifications, offersa promising solution by optimizing quantum circuits while minimizing human effort. However,applying classical program synthesis techniques to quantum computing presents unique chal-lenges across different abstraction levels. The development of novel synthesis and verificationapplications specifically tailored for quantum programming is highly desired.In this thesis, we introduce three novel quantum program synthesis frameworks addressingkey challenges across different levels of quantum computing. First, we present QSynth, the firstframework for synthesizing unitary quantum programs with recursive structures, enabling efficientautomated verification. Second, we introduce MQCC, a quantum meta-programming frameworkthat balances trade-offs among multiple constraints specific to targeted applications and hardware.Finally, we propose NuQes, a neuro-symbolic quantum error correction (QEC) code synthesisframework that leverages heuristic functions generated by large language models (LLMs) tooptimize QEC code design. Together, these frameworks advance quantum program synthesis byimproving efficiency, reducing errors, and enhancing scalability.