# 'Introduction to Quantum Information' Course Page

Hilary Term 2023

Hi all, welcome to C7.4 *Introduction to Quantum Information* taught by
Prof. Artur Ekert. I am the coordinating tutor for the course and I will lay out some general information about the course here.

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 (uploaded 28 Feb 2023) and the notes on
ZX-Calculus (uploaded 03 Mar 2023). 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 and past exam papers below.

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: Shuxiang Cao, Jonathan Classen-Howes, Daniel Zhang or Zhenyu Cai. For any other questions about the course, you can always contact me.

Below we have listed the examinable topics for 2023 for reference.

#### Examinable Topics (2023)

fundamentals of quantum theory: addition of probability amplitudes, quantum interference, mathematical description of states and evolution of closed quantum systems (Hilbert space, unitary evolution), measurements (projectors, Born rule);

definition of quantum entanglement (tensor product structure), Bell states,

quantum gates e.g. phase gate, Hadamard, controlled-not, the Hadamard-phase-Hadamard network, phase “kick-back” induced by controlled-U, phase “kick-back” induced by quantum Boolean function evaluation

Pauli gates, Clifford gates, universal sets of gates, quantum circuits stepping through the execution of quantum circuits

operator norms and distances, approximating unitary operations, the Solovay-Kitaev theorem

no-cloning theorem,

superdense coding, quantum teleportation;

quantum algorithms: Deutsch, Bernstein-Vazirani, Simon

mathematical description of open quantum systems, density matrices, partial trace, Born rule for density matrices

quantum channels, Kraus representation, Choi matrix, completely positive vs positive maps,

Bloch sphere - parametrisation, action of quantum gates on the Bloch vector;

Quantum Error Correction

#### Course Materials

Lecture Videos

Online Lecture Notes (
PDF Version)

Notes on Quantum Error Correction

Notes on ZX-Calculus

Preliminary Materials

#### Problem Sheets

Problem Sheet 0

Problem Sheet 1

Problem Sheet 2

Problem Sheet 3

Problem Sheet 4

#### Past year exams

2015
Exam Paper

2016
Exam Paper

2017
Exam Paper

2018
Exam Paper

2019
Exam Paper

2020
Exam Paper

2021
Exam Paper

#### Fun Reads

Beyond the Quantum Horizon

The Limits of Quantum Computers

Quantum Eraser

Quantum Seeing in the Dark

Quantum Minesweeper