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This conference talk from PLanQC 2025 introduces the Hierarchical Unified Graph Representation (HUGR), a novel graph-based intermediate representation designed specifically for mixed quantum-classical programs. Learn about HUGR's highly expressive and extensible architecture that captures capabilities of both near-term and future quantum computing devices while supporting evolving abstractions from new quantum programming paradigms. Discover how the machine-friendly graph structure enables powerful pattern matching compilation techniques, and how HUGR's MLIR-inspired design allows compilation tooling to work with programs at multiple abstraction levels. The presentation covers HUGR's safety guarantees including strict static typing and linear quantum types that facilitate rapid development of compilation tools without risking program invalidation. Presented by researchers from Quantinuum and the University of Oxford, this 23-minute talk provides insights into this open-source specification and reference implementation for quantum-classical programming.
