Mathematical Institute, University of Oxford
Introduction to Quantum Information
C7.4 · Part C · Hilary Term
The classical theory of computation usually does not refer to physics. Pioneers such as Turing, Church, Post and Goedel managed to capture the correct classical theory by intuition alone and, as a result, it is often falsely assumed that its foundations are self-evident and purely abstract. They are not! Computers are physical objects and computation is a physical process. Hence when we improve our knowledge about physical reality, we may also gain new means of improving our knowledge of computation. From this perspective it should not be very surprising that the discovery of quantum mechanics has changed our understanding of the nature of computation. In this series of lectures you will learn how inherently quantum phenomena, such as quantum interference and quantum entanglement, can make information processing more efficient and more secure, even in the presence of noise.
Syllabus
- 01Quantum interferenceProbability amplitudes, how they add, and why interference is the whole story.
- 02Qubits, gates and circuitsSingle-qubit gates, measurement, and the circuit model of computation.
- 03Entanglement and multi-qubit systemsBell states, correlations no classical account reproduces, and Bell inequalities.
- 04Early quantum algorithmsDeutsch, Bernstein–Vazirani and Simon: where the speed-up actually comes from.
- 05Teleportation and superdense codingEntanglement as a channel resource, and what it can and cannot carry.
- 06Open quantum systemsDensity operators, quantum channels, decoherence and the price of contact with the world.
- 07Quantum error correctionCodes and the stabilizer formalism, up to surface codes and fault tolerance.
Course materials
- Lecture notes — The qubit guide, online, or as a single PDF. The guide goes further than the course; extra topics and exercises there are not examinable.
- Recorded lectures — the full YouTube playlist.
- Prerequisite material (PDF) — the linear algebra and quantum basics assumed from the start.
- Lecture notes (PDF) and slides (PDF) for the guest lectures by Zhenyu Cai. This material is examinable.
- Class arrangements — tutors, classes and announcements for the current term, maintained by Zhenyu Cai, the course coordinator.
Problem sheets
Questions are marked A bookwork, B standard, C challenging or optional. Sheet 0 is a warm-up and is not marked.
- 00Warm-upInformation is physical; binary strings, one-time pad, complex numbers, Dirac notation, complexity.
- 01Gates and interferencePauli and Clifford groups, stabilisers, single-qubit interference, the quantum bomb tester.
- 02Entanglement and mixed statesTwo-qubit gates, entanglement, teleportation, partial trace, trace distance, Bloch vectors.
- 03Bell correlations and algorithmsBell correlations, controlled unitaries, Simon’s algorithm, Deutsch’s algorithm with decoherence.
- 04Channels and error correctionCompletely positive maps, approximate cloning, stabiliser codes, Shor’s nine-qubit code.
Past examination papers
Paper C7.4, Trinity Term. Earlier papers are in the Mathematical Institute archive.
Further reading
- 2012Beyond the quantum horizonDavid Deutsch and Artur Ekert, Scientific American.
- 2008The limits of quantum computersScott Aaronson, Scientific American.
- 2007A do-it-yourself quantum eraserRachel Hillmer and Paul Kwiat, Scientific American.
- 1996Quantum seeing in the darkPaul Kwiat, Harald Weinfurter and Anton Zeilinger, Scientific American.
- BlogQuantum minesweeperBuilding quantum bomb testers and other thought experiments on real quantum computers, Qiskit.