With a Few Square Roots, Quantum Computing is as Easy as Pi

Explore a groundbreaking approach to quantum computing in this 20-minute conference talk from POPL 2024. Delve into how extending rig groupoids with just two maps and three equations can create a computationally universal and equationally sound model of quantum computing. Learn about the semantic model of Π, a universal classical reversible programming language, and its extension √Π, which becomes a fully-fledged quantum programming language. Discover the significance of square roots in this model, including an 8th root of the identity morphism and a square root of symmetry, constrained by a nondegeneracy axiom. Understand how this semantic construction relates to various quantum gate sets, including the Clifford gate set and the computationally universal Gaussian Clifford+T gate set. Gain insights from experts in quantum computing, reversible computing, and programming language theory as they present their innovative research at the intersection of mathematics and computer science.