The fourth Machine Learning for Health (ML4H) symposium was held in person on December 15th and 16th, 2024, in the traditional, ancestral, and unceded territories of the Musqueam, Squamish, and Tsleil-Waututh Nations in Vancouver, British Columbia, Canada. The symposium included research roundtable sessions to foster discussions between participants and senior researchers on timely and relevant topics for the ML4H community. The organization of the research roundtables at the conference involved 13 senior and 27 junior chairs across 13 tables. Each roundtable session included an invited senior chair (with substantial experience in the field), junior chairs (responsible for facilitating the discussion), and attendees from diverse backgrounds with an interest in the session's topic.

Remarkable advances in the past two years have seen quantum computing hardware reach the point where the deployment of quantum devices for nontrivial tasks is now a near-term prospect. However, these machines still suffer from severe limitations, both in terms of memory size and the coherence time of their qubits. It is therefore of paramount importance to extract the most useful work from the fewest operations: a poorly optimised quantum program may not be able to finish before it is undone by noise. In this paper we study the automated optimisation of Clifford circuits. Clifford circuits are not universal for quantum computation - they are well known to be efficiently simulable by a classical computer [2] - however adding any non-Clifford gate to the Cliffords yields a set of approximately universal operations hence it is likely that the vast majority of operations in any quantum program will be Clifford operations, and hence reducing the Clifford depth and gate count of a circuit will have substantial benefit.

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.