Quantum Information (winter term 2016/17)

Lecture "Quantum Information" (winter term 2016/17)

Lecturer: Norbert Schuch

Overview

Quantum Information is concerned with the study of quantum mechanics from the point of view of information theory, as well as with the use of quantum mechanical systems for the purpose of information processing and computation. On the one hand, this includes quantum information theory, with topics such as quantum teleportation, the transmission of information through quantum channels, quantum cryptography, and the quantification of quantum entanglement as a resource for the aforementioned tasks. On the other hand, it involves quantum computation, i.e., computation based on the laws of quantum mechanics, covering topics such as quantum algorithms, quantum error correction, and the physical realization of quantum computers.

This lecture will provide a comprehensive introduction to the field of Quantum Information. Planned topics include

States, evolution, and measurement
Quantum entanglement
Quantum channels
Quantum cryptography
Quantum computation and quantum algorithms
Quantum error correction
Implementations of quantum information processing

Prerequisites

Solid knowledge of Linear Algebra is essential for this lecture. Knowledge of quantum mechanics is useful, but not necessary. (However, please let me know in advance if you have no prior knowledge of quantum mechanics.)

Material

Lecture notes

Lecture 1 (28.10., 2hrs): I. Introduction.
II. The formalism: States, measurements, evolution. Pure states, unitary evolution, projective measurements. Composite systems.
Lecture 2 ( 4.11., 2hrs): II. The formalism: States, measurements, evolution. Mixed states. The Schmidt decomposition and purifications.
Lecture 3 (11.11., 2hrs): II. The formalism: States, measurements, evolution. POVM measurements. General evolution: Superoperators.
Lecture 4 (25.11., 2hrs): III. Entanglement. Introduction. Bell inequalities. Applications of entanglement: Teleportation, Dense coding.
Lecture 5 ( 2.12., 2hrs): III. Entanglement. Entanglement conversion and quantification. (See also this review by Nielsen and Vidal).
Lecture 6 ( 9.12., 2hrs): III. Entanglement. Mixed state entanglement.
Lecture 7 ( 13.1., 3hrs): IV. Quantum Computation. The circuit model. Oracle-based algorithms.
Lecture 8 ( 27.1., 3hrs): IV. Quantum Computation. Grover's algorithm. The Quantum Fourier transform, period finding, and Shor's algorithm.
V. Quantum Error Correction. Introduction. The 9-qubit Shor code.
Lecture 9 ( 3.2., 2hrs): V. Quantum Error Correction. Quantum Error Correction Conditions. Stabilizer codes.
Lecture 10 (10.2., 2hrs): VI. Implementations of Quantum Information Processing.

Exercise sheets

Exercise Sheet 1 (covers Lecture 1, discussed 4.11.), Solutions
Exercise Sheet 2 (covers Lecture 2+3, discussed 25.11.), Solutions
Exercise Sheet 3 (covers Lecture 4+5, discussed 9.12.), Solutions
Exercise Sheet 4 (covers Lecture 6+7, discussed 20.1.), Solutions
Exercise Sheet 5 (covers Lecture 8+9, discussed 10.2.), Solutions

Literature

Main texts

J. Preskill, Quantum Computation lecture notes.
M. Nielsen and I. Chuang, Quantum Information and Computation. (Cambridge University Press, 2010)

Other lecture notes: Mark Wilde, Reinhard Werner

Further reading:

A. Peres, Quantum Theory: Concepts and Methods (Kluver Academic Press, 2002)

Organisatorial issues

The lecture takes place Friday 14:00-16:00 (on 13.1. and 27.1. from 14:00-17:00) in room PH2271. In compensation for the lecture being 120 min rather than 90 min, some Fridays will be off (this will be announced during the lecture and on this website).

Tutorials for the lecture are offered on a voluntary basis. The tutorials take place every second Friday after the lecture, starting Nov. 4th, and will be given by Mohsin Iqbal. Exercise sheets will be posted the Monday before the tutorial.