# 'Introduction to Quantum Information' Course Page

Hilary Term 2022

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. 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 section on quantum error correction in the lecture notes is still a work in progress, so I’ve prepared
some notes introducing some of its core concepts. Note that the lecture notes contain some additional exercises beyond the problem sheets and also some *non-examinable* topics that are mainly of interest.

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). All examinable topics are covered in the lecture videos.

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. For a deeper dive into the example, one of our tutors Maria has kindly prepared an informative video with an accompanying blog post. In fact, this is actually one of the problems that you’ll encounter in Problem Sheet 1. You may also be interested in the great events and talks hosted by the Oxford University Quantum Information Society.

If you have any questions about the tutorial classes, don’t hesitate to get in touch with the tutor of your class: Aleksandra Ziolkowska, Maria Violaris or Zhenyu Cai. For any other questions about the course, you can always contact me.

In Artur’s last lecture he mentioned that everything covered in his lectures is examinable except quantum error correction, which was not covered properly due to time constraint. Below we have listed the examinable topics for 2022 for reference.

#### Examinable Topics (2022)

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;

basics of quantum cryptography; quantum key distribution using entangled state.

#### Course Materials

Lecture Videos

Online Lecture Notes (
PDF Version)

Preliminary Materials

Notes on Quantum Error Correction

#### Problem Sheets

Problem Sheet 0
Solutions

Problem Sheet 1
Solutions

Problem Sheet 2
Solutions

Problem Sheet 3
Solutions

Problem Sheet 4
Solutions

#### 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