It's been a little more than 40 years since researchers first suggested exploiting quantum physics to build more powerful computers. During this time, we have seen the development of many quantum algorithms and significant technological advances to make these devices. As a result, at this point, large-scale quantum computers, capable of providing valuable solutions to complex problems, seem like a certainty, even if still distant.

Nonetheless, there is a great gap between the communities of quantum algorithms and quantum devices researchers. On the one hand, algorithm designers most often describe algorithms in a high level of abstraction, using a mixture of natural language, pseudocode, and mathematical formulas---a form deriving asymptotic complexity estimates while shielding researchers from the low-level complexities and restrictions. On the other hand, physical devices only understand algorithms implemented using the primitive low-level abstractions they support.

Most programming systems available for quantum computing are intertwined with the quantum circuit model, so developers must implement algorithms in terms of low-level unitary operators. Not surprisingly, the implementation of quantum algorithms on such a low level of abstraction is very time-consuming, error-prone, and results in non-portable programs---given the technological diversity of quantum devices.

In this thesis, I study problems related to the compilation of quantum programs, seeking forms of augmenting the expressive power of current frameworks and narrowing the gap between algorithmic research and concrete implementations. I focus on scalability and practicality---in particular, together with theoretical investigations, I developed concrete algorithms that are performant and scalable. The embodiment of my research contribution is a compiler companion library for the synthesis and compilation of quantum circuits called tweedledum.