Quantum Computing Tutorial with Bob Coecke (Oxford)

Quantum information processing: a new light on the quantum formalism and quantum foundations

In these lectures we survey the key examples of quantum information processing, which include protocols such as quantum teleportation and dense coding, the main quantum algorithms such as Grover's and Shor's, quantum key distribution protocols such as BB84 and Ekert91, as well as non-standard quantum computational models such as measurement-based quantum computing. We discuss how these pose a new challenge for an operational account on quantum foundations. These foundational considerations point at a new avenue in the quest to find a more appropriate language to describe quantum phenomena, a challenge posed by John von Neumann merely 3 years after his publication of the Hilbert space quantum mechanical formalism in 1932, which has led to the the (failed) program of Birkhoff-von Neumann quantum logic, his continuous geometries, as well as his important contributions in operator algebras. We show how ideas from type theory, categorical logic, linear logic and graph theory contribute to such a high-level quantum formalism.