Quantum Computing (University of Cambridge)

The University of Cambridge makes materials for its undergraduate Quantum Computing course freely available online through the Department of Computer Science and Technology. This includes the full set of lecture notes from the 2023-2024 academic year, when the course was delivered as sixteen lectures by Dr Steven Herbert. The course is taught at a level appropriate for students with a mathematics or computer science background and provides a rigorous introduction to quantum computing without assuming prior knowledge of quantum mechanics.

The curriculum follows the standard arc of a university-level introduction: it begins with the mathematics of qubits and quantum states, builds up to quantum circuits and the mechanics of measurement, introduces entanglement and its consequences, and then covers the major quantum algorithms that motivate the field. Shor’s algorithm and Grover’s algorithm receive serious treatment, with the mathematical reasoning developed rather than just the high-level story. Quantum cryptography, including the BB84 protocol and its security argument, is covered as a concrete application of quantum information principles.

Cambridge lecture notes are notable for their precision and depth relative to MOOC-style courses. The writing is dense and rewards careful reading. For a self-directed learner who wants to understand the subject properly rather than pick up a surface-level familiarity, working through these notes is a highly effective approach. The course pages are updated for each academic year and reflect the current state of a well-maintained undergraduate curriculum.

What you’ll learn

• The mathematical description of qubit states: Dirac notation, state vectors, and the Bloch sphere
• Superposition and measurement: the Born rule and what happens when you measure a quantum state
• Quantum gates and circuits: unitary operations, reversibility, and circuit composition
• Entanglement: definition, preparation, and why it cannot be explained by classical correlations
• Grover’s algorithm: the quadratic speedup for unstructured search and why it is optimal
• Shor’s algorithm: the connection to period finding and why it threatens RSA encryption
• Quantum cryptography: the BB84 key distribution protocol and its security guarantee

Who is this for?

• Students who want a rigorous university-level introduction without enrolling in a university course
• Anyone who found MOOC treatments of quantum computing too shallow and wants something more precise
• Mathematics and computer science graduates who learn well from written lecture notes
• Self-directed learners who want to understand the formal arguments behind quantum algorithms, not just the intuitions