Lecture: Quantum Information


Lecturer: Norbert Schuch


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


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.)


Lecture notes and exercise sheets will be posted on this website. The L2P system will be primarily used for email communications.

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

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.)
Main texts:

Other lecture notes: Mark Wilde, Reinhard Werner, Michael Wolf (in German)

Further reading:

Organisatorial issues

The lecture takes place Thursday 12:15-13:45 in 26C401, and Friday 12:15-13:45 in 28B110. The tutorial takes place Monday 12:15-13:45 in 28B110, starting on April 27th.

Exercise sheets are posted on this website every Friday. Solutions should be handed in by the following Thursday, and will be discussed the following Monday. Tutorials are given by Mohsin Iqbal, and the problem sets are prepared by Anna Vershynina. 50% of the points for the exercise sheets are prerequisites for the admission to the exam, which will be an oral exam of 40 minutes.

There is an L2P site for the lecture, which will be primarily used to send out communications. Lecture notes and exercise sheets will be posted on this website.