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Explore a groundbreaking approach to quantum program semantics in this 14-minute conference talk from PLanQC 2026. Discover how researchers Robert I. Booth and Cole Comfort from the University of Oxford and INRIA Paris-Saclay develop a sound, universal, and complete denotational semantics specifically for stabiliser quantum programs. Learn about their innovative interpretation of quantum operations as affine relations, which provides a significantly simpler alternative to traditional operator-algebraic semantics. Understand how this framework incorporates measurement and classical control while treating quantum error-correcting codes as first-class objects within the stabiliser fragment of quantum theory. Examine the practical applications through their proof-of-concept assembly language for stabiliser programs that features fully-abstract denotational semantics, demonstrating the foundational importance of stabiliser operations in quantum error correction and fault-tolerant quantum program compilation.
