Section: General | C7.4 Introduction to Quantum Information (2025-26)

Lecturer: Profile: Zhenyu Cai
Lecturer: Profile: Artur Ekert

Course information

General prerequisites:

Quantum Theory.
The course material should be of interest to physicists, mathematicians, computer scientists, and engineers. The following will be assumed as prerequisites for this course:
- elementary probability, complex numbers, vectors and matrices;
- Dirac bra-ket notation;
- a basic knowledge of quantum mechanics especially in the simple context of finite dimensional state spaces (state vectors, composite systems, unitary matrices, Born rule for quantum measurements);
- basic ideas of classical theoretical computer science (complexity theory) would be helpful but are not essential.
Prerequisite notes will be provided giving an account of the necessary material. It would be desirable for you to look through these notes slightly before the start of the course.

Course term: Hilary

Course lecture information: 16 lectures

Course weight: 1

Course level: M

Assessment type: Written Examination

Course overview:

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.

Learning outcomes:

By the end of the course, students will be able to:

Use single qubit and two qubits quantum logic gates to construct quantum circuits of increasing complexity.
Provide comparative analysis of quantum and classical algorithms.
Solve problems involving quantum entanglement and its applications.
Perform calculations using density matrices and completely positive maps.
Use mathematical techniques that protect quantum evolutions, such as quantum error correction and fault tolerant computation.

Course synopsis:

Bits, gates, networks, Boolean functions, reversible and probabilistic computation
"Impossible" logic gates, amplitudes, quantum interference
One, two and many qubits
Entanglement and entangling gates
From interference to quantum algorithms
Algorithms, computational complexity and Quantum Fourier Transform
Phase estimation and quantum factoring
Non-local correlations and cryptography
Bell's inequalities
Density matrices and CP maps
Decoherence and quantum error correction

Section outline

Select section General
- Select activity Announcements
  
  Announcements Forum
- Select activity Reading List
  
  Reading List URL
- Select activity Discussion Forum
  
  Discussion Forum
- Select activity More Info
  
  More Info URL
- Select activity 'Introduction to Quantum Information' Course Page
  
  Introduction to Quantum Information Course Page
  
  The course lecture notes are available online and also in PDF. Note that the lecture notes contain some additional exercises beyond the problem sheets and also some non-examinable topics that are mainly of interest. For the guest lectures, here are the links to the notes on Quantum Error Correction. Note that the materials in the guest lectures are examinable.
  
  There are some preliminary materials on the basic concepts for the course, which overlap with parts of the lecture notes but nevertheless can be helpful to read through.
  
  The accompanying lecture videos are embedded in the online version of the book, but they can also be found as a standalone series on Youtube (in a slightly different order). Not all topics in the videos are examinable. In particular, lecture 8 of the videos covers topics in Quantum Error Correction that are not covered in the lectures like the quantum error correction criterion. They are not examinable, but nonetheless these are very interesting concepts to explore.
  
  You can find the problem sheets for this course below, and all past papers can be found here.
  
  In addition, there are some interesting perspective pieces to be read at your leisure, to have a glimpse into different ways to harness the power of the quantum wizardry. One of the most fascinating examples is the Quantum Bomb Tester, a way to detect an ultra-sensitive (maybe an understatement) bomb without setting it off. In fact, this is actually one of the problems that you’ll encounter in Problem Sheet 1.
  
  If you have any questions about the tutorial classes, don’t hesitate to get in touch with the tutor of your class: Christian Binder, Muhammad Hamza Waseem and Po-Wei Huang. For any other questions about the course, you can always contact me.
- Select activity Fun Reads
  
  Fun Reads
  
  Beyond the Quantum Horizon
  The Limits of Quantum Computers
  Quantum Eraser
  Quantum Seeing in the Dark
  Quantum Minesweeper

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Section outline