Quantum computing leverages the quantum properties of subatomic matter to enable algorithms to run faster than those possible on a regular computer. Quantum computers have become increasingly practical in recent years, with some small-scale machines available for public use. Quantum computing applications are largely dependent on the software that manipulates computations on the hardware. These applications rely on a variety of symbolic representations including quantum programs to describe and manipulate quantum information effectively. However, quantum programs are notoriously difficult to code and verify due to the unintuitive quantum knowledge associated with quantum programming. Automated tools that relieve the tedium and errors associated with low-level quantum details are highly desirable.

This thesis focuses on developing theoretical and practical tools to automatically synthesize desired quantum programs in the different quantum application domains. I first present QSynth, the first quantum program synthesis framework that initiates the study of program synthesis for unitary quantum programs with recursive structure. Then, I present MQCC, the first general-purpose quantum meta-programming framework that helps programmers balance trade-offs among a large number of factors specific to the targeted application and quantum hardware. Finally, I present a NeUrosymbolic Quantum Error correction code Search framework (NuQes) for synthesizing quantum error correction code with a low logical error rate and high encoding rate, guided by the heuristic function generated by LLM.

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