Lecture and tutorial classes

Quantum computing and characterization of quantum devices

(Summer term 2022)

Quantum computing is among the most exciting applications of quantum mechanics. Quantum algorithms can solve computational problems efficiently that have a prohibitive runtime on traditional computers. Such problems include, for instance, factoring of integer numbers or energy estimation problems from quantum chemistry.

This course provides an introduction to quantum computing and discusses some challenges ahead.

An emphasize will be put on conceptual and mathematical aspects.

Content

  • Information theoretic introduction to quantum mechanics

  • The unitary circuit model of quantum computation
    (qubits, quantum gates and readout)

  • Basic algorithms

  • The quantum Fourier transform and Shor's algorithm for integer factoring

  • Simulation of complex quantum systems

  • Characterization of quantum computing components

  • Selected advanced topics

Exercises and other files will be uploaded here, password in the lecture or on email request.

Also lecture notes will be uploaded.

Formal things

Lecture and tutorial class

  • Tuesday 12:30, Hörsaal 2531.HS 5K

  • Thursday 12:30, Hörsaal 2522.HS 5H

  • This is an in-person course. Additional streaming of the lecture might be offered via Webex, see lecture notes.

  • Prerequisites: linear algebra, complex numbers

  • Helpful but not strictly required

    • Quantum mechanics

    • Basics in computer science

    • Basics in quantum information theory

  • Assignments will be uploaded roughly every two weeks. The solutions to the assignment sheets need to be handed in. At least 75% of the sheets need to be finished as a prerequisite for the exam. There will be no corrections but the solutions will be discussed in the tutorial classes.
    Collaboration policy: Collaborations are only allowed, if they are disclosed on the exercise submissions.

Preliminary schedule

April

05 L01 Motivation, course outline, formalities Exercise 1 handed out
07 L02 Review of linear algebra
12 L03 Quantum mechanics I Due date for Ex. 1; Ex. 2 handed out
14 T1 Discussion Ex. 1
19 L04 QM II (measurements) Due date for Ex. 2; Ex. 3 handed out
21 T2 Discussion Ex. 2
26 L05 QM III (tensor product) Due date for Ex. 3; Ex. 4 handed out
28 T3 Discussion Ex. 3


May

03 L06 No cloning, reversibility
05 L07 Superdense coding, q. teleportation
10 L08 Hybrid; Classical computation Due date for Ex. 4.1-4.2; Ex. 5 handed out
12 T4 Discussion Ex. 4.1-4.2
17 L09 Classical computation Due date Ex. 4.3, 4.4, 5; Ex. 6 handed out
19 T5 Discussion Ex. 5 + 4.3,4.4
24 L10 Simple q. algorithms
26 - Public holiday
31 L11 Simple q. algorithms *Due date for Ex. 6; Ex. 7 handed out


June

02 T6 Discussion Ex. 6
07 L12 QFT
09 L13 QPE Due date for Ex. 7; Ex. 8 handed out
14 T7 Discussion Ex. 7
16 - Public holiday
21 L14 Shor Due date Ex. 8; Ex. 9 handed out
23 L15 Shor
28 T8 Discussion Ex. 8
30 L16 TBA


July

05 L17 TBA Due date Ex. 9
07 T9 Discussion Ex. 9
12 E Exam?
14 L18 TBA