Introduction to Quantum Computing (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. The introductory course reflects this pedigree: it is mathematically precise, grounded in computer science theory, and structured to develop genuine understanding rather than surface familiarity.

The course approaches quantum computing from the perspective of a computer scientist rather than a physicist. The emphasis is on computation: what problems can quantum computers solve, how efficient are the solutions, and what does quantum speedup actually mean in a complexity-theoretic sense. Students who come from a physics background will find this a useful complement to courses that emphasize the physical realization of quantum systems.

What you’ll learn

The course begins with the circuit model of quantum computation, developing the gate set and the rules for constructing and reasoning about quantum circuits. Basic quantum phenomena, superposition, interference, and entanglement, are introduced in terms of their computational roles rather than their physical interpretations. The Deutsch-Jozsa and Bernstein-Vazirani algorithms are used as early examples to show how quantum interference can be exploited to solve problems with fewer queries than any classical algorithm.

Grover’s search algorithm is covered in depth, including the geometric interpretation of amplitude amplification and the proof of optimality. Shor’s factoring algorithm is developed carefully, with the classical number theory and quantum phase estimation components treated separately before being combined. The course closes with quantum complexity theory: the classes BQP and QMA, oracle separations, and the relationship between quantum and classical computational complexity.

Who is this for

This course suits computer science students at the advanced undergraduate or graduate level who want a rigorous treatment of quantum computing grounded in complexity theory. It is also appropriate for mathematicians and physicists who are comfortable with abstract reasoning and want to understand quantum computing as a theoretical discipline. Software engineers with strong CS fundamentals will find the circuit-model framing accessible.

Prerequisites

Comfort with linear algebra is essential: vectors, matrices, eigenvalues, and unitary transformations are used from the start. Familiarity with classical algorithms and computational complexity, including Big-O notation and complexity classes, is assumed. No physics background is required. Prior exposure to probability theory is helpful for understanding measurement and sampling.