Lecture "Quantum Information"(summer term 2015)

Lecturer: Norbert Schuch

(This is a mirror copy of the original course website at RWTH Aachen.)

Overview

Prerequisites

Material

Lecture notes

• Lecture 1 (13.4.): I. Introduction.
• Lecture 2 (16.4.): II. Formalism. Pure states, unitary evolution, projective measurements.
• Lecture 3 (17.4.): II. Formalism. Mixed states.
• Lecture 4 (20.4.): II. Formalism. Schmidt decomposition & purifications. POVM measurements.
• Lecture 5 (23.4.): II. Formalism. Superoperators, Kraus representation, Choi-Jamiolkowski isomorphism.
• Lecture 6 (24.4.): III. Entanglement. Introduction. Bell inequalities.
• Lecture 7 (30.4.): III. Entanglement. Applications: Superdense coding, teleportation.
• Lecture 8 (7.5.): III. Entanglement. Entanglement conversion and quantification: Single-copy conversion and majorization. (See also this review by Nielsen and Vidal).
• Lecture 9 (8.5.): III. Entanglement. Entanglement conversion and quantification: Asymptotic protocols.
• Lecture 10 (15.5.): III. Entanglement. Mixed state entanglement.
• Lecture 11 (21.5.): III. Entanglement. Quantification of mixed state entanglement.
  IV. Quantum Computation. The circuit model.
• Lecture 12 (22.5.): IV. Quantum Computation. The circuit model. Oracle-based algorithms.
• Lecture 13 (5.6.): IV. Quantum Computation. Oracle-based algorithms. Grover's algorithm.
• Lecture 14 (11.6.): IV. Quantum Computation. The quantum Fourier transform, period finding, and Shor's factoring algorithm.
• Lecture 15 (12.6.): V. Quantum Error Correction. Introduction. The 9-qubit Shor code.
• Lecture 16 (18.6.): V. Quantum Error Correction. Quantum error correction conditions & properties of Quantum Error Correcting Codes. Classical Codes.
• Lecture 17 (19.6.): V. Quantum Error Correction. Classical Codes. CSS codes. Stabilizer codes.
• Lecture 18 (25.6.): V. Quantum Error Correction. Stabilizer codes. (See also these lecture notes by Dave Bacon.)
• Lecture 19 (26.6.): VI. Implementations of quantum computing. Requirements for quantum computing architectures.
• Lectures 20 and 21 (2./3.7., guest lectures by D. DiVincenzo): VI. Implementations of quantum computing. Superconducting qubits. Spin qubits.
• Lecture 22 (9.7.): VII. Quantum Cryptography.
• Lecture 23 (10.7.): VIII. Quantum Complexity Theory. Classical complexity classes. Quantum complexity classes.
• Lecture 24 (16.7.): VIII. Quantum Complexity Theory. Quantum Complexity Classes. QMA-completeness of the k-local Hamiltonian problem.
• Lecture 25 (17.7.): IX. Topological Quantum Memories and Quantum Computing. The Toric Code. Toric Code as a topological model.

Lecture notes, merged by chapter

• I. Introduction
• II. Formalism
• III. Entanglement
• IV. Quantum Computation
• V. Quantum Error Correction
• VI. Implementations of quantum computing
• VII. Quantum Cryptography
• VIII. Quantum Complexity Theory
• IX. Topological Quantum Memories and Quantum Computing

Exercise sheets

• Exercise Sheet 1 (due 23.4., discussed 27.4.)
• Exercise Sheet 2 (due 30.4., discussed 4.5.)
• Exercise Sheet 3 (due 7.5., discussed 11.5.)
• Exercise Sheet 4 (due 15.5., discussed 18.5.)
• Exercise Sheet 5 (due 21.5., discussed 8.6.)
• Exercise Sheet 6 (due 5.6., discussed 8.6.); Solutions.
• Exercise Sheet 7 (due 11.6., discussed 15.6.)
• Exercise Sheet 8 (due 18.6., discussed 22.6.)
• Exercise Sheet 9 (due 25.6., discussed 29.6.)
• Exercise Sheet 10 (due 2.7., discussed 6.7.)
• Exercise Sheet 11 (due 8.7., discussed 13.7.)

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, Michael Wolf (in German)

Further reading:

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

Organisatorial issues