The Quantum Applications of Abstract Multi Linear Algebra
In this lecture Gyula Rábai explores how abstract multi-linear algebra provides the mathematical backbone of modern quantum theory and quantum computing. Beginning with foundational structures such as sets, magmas, groups, fields, and vector spaces, it builds an intuitive pathway from basic algebraic ideas to quantum concepts. The talk explains how vectors, bases, and linear combinations naturally describe physical phenomena like photon polarization and quantum superposition. Key quantum principles—such as probability amplitudes, global phase, and measurement—are connected directly to linear algebraic structure. The lecture then shows how tensor products, rather than direct sums, define multi-qubit systems and give rise to exponential state spaces. By bridging abstract algebra and physical intuition, he reveals why quantum systems behave so differently from classical ones and how this difference powers quantum computation.
This presentation was given to:
Mathematics Society, Colchester Grammar School, 17th September 2025
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