# 'Introduction to Quantum Information' Course Page

Hilary Term 2024

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 2024). 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: Zhenghao Zhong, Tim Hosgood, Bálint Koczor. For any other questions about the course, you can always contact me.

Below we have listed the examinable topics for 2024 for reference.

#### Examinable Topics (2024)

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 (orthogonal projectors, Born rule).

Fundamentals of computer science: binary strings, bit-by-bit addition of binary strings, computational complexity, basic computational complexity classes P, NP, EXP, BPP, BQP.

Elementary single-qubit quantum gates: phase gate, Hadamard gate, T gate.

Single-qubit interference: Hadamard-phase-Hadamard circuit.

Controlled-not gate, the notion of quantum entanglement (tensor product structure), Bell states.

Phase “kick-back” induced by controlled-U, phase “kick-back” induced by quantum Boolean function evaluation.

Pauli gates, Clifford gates, universal sets of gates, Hadamard transform on many qubits.

Quantum circuits and stepping through the execution of basic quantum circuits.

No-cloning theorem, quantum teleportation.

Bell inequalities and their violation.

Basic quantum algorithms: Deutsch, Bernstein-Vazirani, Simon.

Mathematical description of open quantum systems, density matrices, partial trace, Born rule for density matrices, representing density operators in terms of statistical mixtures of pure states.

Bloch sphere - representing a single qubit density operator in terms of the Bloch vector, action of quantum gates on the Bloch vector.

Quantum channels, isometry, Kraus representation, unitary equivalence of different Kraus representations.

Completely positive vs positive maps, examples of positive but not completely positive maps.

Criteria for reversible/correctable quantum channels.

Basic concepts of quantum error correction, code, code distance, error syndrome.

Parity checks: X-checks and Z-checks, Tanner graphs.

Stabilisers, stabiliser group.

#### Course Materials

Lecture Videos

Online Lecture Notes (
PDF Version)

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