Quantum Processes and Computation (Oxford)

Oxford’s computer science department has one of the longest-standing quantum computing research groups in the world. The Quantum Group at Oxford, associated with figures including Bob Coecke and Samson Abramsky, has contributed foundational work to the categorical and diagrammatic foundations of quantum computation. This course, Quantum Processes and Computation, taught by Aleks Kissinger over 24 lectures in Michaelmas term, reflects that pedigree directly: it is built around the diagrammatic approach developed at Oxford and structured to develop genuine understanding rather than surface familiarity.

The course approaches quantum theory from the perspective of a computer scientist rather than a physicist. Instead of starting from Hilbert spaces and wave functions, it develops quantum theory as a theory of processes, using string diagrams and the ZX-calculus to reason about composition, entanglement, and computation. Students who come from a physics background will find this a useful complement to courses that emphasize the physical realization of quantum systems. Note that formal enrollment is limited to Oxford students, but the full handwritten lecture notes are publicly available on the course page, and the primary textbook is Coecke and Kissinger’s Picturing Quantum Processes.

What you’ll learn

The course begins with string diagrams: parallel and sequential composition of processes, transposes, adjoints, and the diagrammatic treatment of unitarity and inner products. Core quantum phenomena, entanglement, Bell states, quantum teleportation, and the no-cloning theorem, are derived in terms of their computational and compositional roles rather than their physical interpretations. From there it covers measurements (von Neumann and POVM), dense coding, entanglement swapping, and the interaction between classical and quantum data.

The second half develops the ZX-calculus, including its universality and completeness for stabiliser quantum mechanics, along with complementarity and quantum key distribution. The course then connects this machinery to the circuit model of quantum computing and quantum algorithms, including Deutsch-Jozsa, quantum search, and the hidden subgroup problem, and closes with measurement-based quantum computation (MBQC), quantum non-locality, and resource theories of entanglement.

Who is this for

This course suits computer science students at the advanced undergraduate or graduate level who want a rigorous treatment of quantum computation grounded in compositional, diagrammatic reasoning. It is also appropriate for mathematicians and physicists who are comfortable with abstract reasoning and want to understand quantum theory as a theory of processes. Self-learners working from the public lecture notes and the Picturing Quantum Processes textbook can follow the same material.

Prerequisites

Comfort with linear algebra is essential: vectors, matrices, eigenvalues, and unitary transformations are used throughout, even though the diagrammatic notation often replaces explicit matrix calculations. General mathematical maturity and comfort with abstract, compositional reasoning are assumed. No physics background is required. Prior exposure to probability theory is helpful for understanding measurement and sampling.