MBQC and the ZX-Calculus

Sept 2024 – July 2025 · Centre INRIA de Nancy · MOCQUA team · Supervised by Dr Miriam Backens

Report (PDF) · Slides (PDF)

A year-long research project carried out alongside my studies at École des Mines, roughly 1.5 days per week, through the school’s Parcours Recherche track.

As this was my first real encounter with quantum computing, the project first involved learning its fundamentals. I then studied the ZX-calculus — a graphical language for reasoning about quantum computation, the Measurement-Based Quantum Computing (MBQC) paradigm, and how the former can help describe the latter. From that point, my supervisor asked me to look at flows, which are mathematical conditions involving graph-theory that guarantee a measurement pattern can be run deterministically, despite measurement outcomes being random. Underlying one of the versions of flow is the notion of focussed sets, which I had to look into for the rest of the project. My goal was to understand their properties, including their interpretation and practical role. This implied pen-and-paper work but also programming and some contribution to unpublished code used for understanding these objects. The project didn’t lead to a publication, but it gave me my first experience in research and pushed me to continue with a research-oriented master’s programme in quantum.