# Quantum Information: 2019-2020

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| Schedule S1(CS&P) — Computer Science and Philosophy |

| Hilary Term 2020 (16 lectures) |

## Overview

The aim of this course is to introduce the key concepts and methods of Quantum Information and Computation.

The course is designed for computer science undergraduates and focuses on the general theory of quantum information, independently of the physical realizations. The course is divided into four parts. The first part provides working knowledge on the mathematical framework of Quantum Theory. The second part focuses on the key operational features of quantum theory, including quantum steering, dense coding, and non-local games. The third part introduces the circuit model of quantum computation, the notions of quantum computational complexity and quantum query complexity, and basic quantum algorithms such as Grover’s algorithm for unstructured search and Shor’s algorithm for polynomial-time factoring. The fourth part concludes the course with an overview of quantum communication and quantum cryptography. The material taught in class is supplemented by a complete set of lecture notes and by the reference textbooks "Quantum Computation and Quantum Information" (M.A. Nielsen and I.L. Chuang, Cambridge University Press), and “Quantum Computer Science” (N. D. Mermin, Cambridge University Press).

The lectures for this course are recorded, and the recordings released at the end of each week of term. Please click here to access the recordings.

## Learning outcomes

1) Understand the fundamentals of quantum theory, including quantum states, evolutions, and measurements 2) Be able to model computation and communication tasks in the quantum model 3) Posses the basics of quantum algorithms, including the techniques of amplitude amplification and the quantum Fourier transform 4) Understand the foundations of quantum communication and cryptography## Prerequisites

Essential: Linear Algebra, Discrete Mathematics.

Recommended: Models of Computation, Computational Complexity, Design and Analysis of Algorithms.

## Synopsis

The course is structured as follows, for a total of 16 lectures:

1. **Course overview**: introduction to the subject and practical matters. (1 lecture)

2. **The basic rules of Quantum Theory**: pure states, basic measurements, unitary evolutions, and composite systems (4 lectures)

3. **Key operational features**: quantum steering, dense coding, and non-local games (3 lectures)

4. **Quantum Computation:** the quantum circuit model, quantum computational complexity, quantum query complexity, quantum algorithms (4 lectures)

5. **Quantum communication and cryptography: **no cloning and no-information without disturbance, quantum key distribution, quantum teleportation (4 lectures)

## Syllabus

Bits vs qubits, quantum states, basic measurements, and gates. Composite systems, entanglement and non-local games.

Quantum circuits, quantum computational complexity, quantum query complexity, Grover’s algorithm, Shor’s algorithm.

No-cloning, no-information without disturbance, quantum key distribution, quantum teleportation.

## Reading list

-Course Lecture Notes (primary course material)

-M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2001)

-N. D. Mermin, Quantum Computer Science, Cambridge University Press (2008).