### Challenges in Compiling Hybrid Programs

## Bridging the quantum-classical gap

## Syndrome extraction: an expensive operation #

Benchmark classical code, with and without optimisations enabled. -> Motivate the need for classical compiler optimisations.

## Programming languages and Internal Representations

An important point we have been ignoring: how do we even express and represent hybrid programs?

## Guppy #

## Internal representations #

## Limitation of Existing Techniques

Possibly split into

## Classical Optimisation #

## Quantum Optimisation #

## Equality Saturation: A Promising Solution?

## Term rewriting with equality saturation is the most promising technique #

## Description of eqsat #

## No-clone makes it impossible to use in quantum! Problems with DAGs #