Course syllabus
Course-PM
MCC180 Open quantum systems lp4 VT24 (7.5 hp)
The course is offered by the department of Microtechnology and Nanoscience in English.
The lectures take place in hbar C511 at MC2, if nothing else is communicated.
Contact details
- Göran Johansson, goran.l.johansson@chalmers.se
- Thilo Bauch, thilo.bauch@chalmers.se
- Timo Hillmann, hillmann@chalmers.se
Course purpose
Realistic descriptions of systems used for quantum technologies need to include imperfections, originating from remaining weak interactions with uncontrolled parts of the environment. The effects of such imperfections are often described using Lindblad master equations, determining the time evolution of the system’s density matrix. The purpose of this course is to go through both a microscopic derivation of these equations as well as to give examples of the most common uses of these equations in practical quantum systems. The examples include a practical laboratory session on a system used for quantum technology, e.g. experimentally determining coherence properties of a small superconducting quantum circuit, to complement the theoretical description with hands-on experience.
Schedule
Course literature
"The theory of open quantum systems", H.-P. Breuer and F. Petruccione, Oxford University Press
Course design
Preliminary course schedule, to be adjusted for 2024
Lectures W1 (week 12)
Mon Lecture 1 13:15-15:00
Introduction to Open Quantum Systems
Introduce density matrices
Thursday Lecture 2 10:00-11:45
Introducing Lindblad Master equation
Friday Lecture 3 15:15-17:00
General derivation from weak coupling to a bath
Lecture W2 (week 13)
Mon Lecture 4 13:15-15:00
Quantizing Electrical Circuits
Easter Self Studies (week 14)
Lecture W3 (week 15)
Monday Lecture 5 13:15-15:00
Quantizing Electrical Circuits 2 (LC + JJ + Transmission)
Monday Exercise 1 15:15-17:00
To be determined
Thursday Lecture 6 10:15-12:00
Quantizing Electrical Circuits 3 (LC + JJ + Transmission)
Friday Exercise 2 15:15-17:00
To be determined
Lecture W4 (week 16)
Monday Lecture 5 13:15-15:00
Introducing Bloch equations and expressions for T1 and T2
Wednesday Lecture 6 13:15-15:00
SPAM errors and randomized bench-marking
Friday Exercise 3 15:15-17:00
To be determined
Lecture W5 (week 17)
Mon Lecture 7 13:15-15:00
Input- and output operators, coherent states and the damped harmonic oscillator
Thursday Lecture 8 08:00-09:45
Quantum Trajectories 1
Thursday Exercise 4 10:00-11:45
To be determined
Lecture W5 (week 18)
Mon Lecture 9 13:15-15:00
Quantum Trajectories 2
Thursday Lecture 10 08:00-09:45
Input-output formalism 1
Thursday Lecture 11 10:00-11:45
Input-output formalism 2
Friday Lecture 12 15:15-17:00
Weak measurements 1
Lecture W6 (week 19)
Mon Exercise 5 13:15-15:00
To be determined
Lecture W7 (week 20)
Monday Lecture 13 13:15-15:00
Weak measurements 2
Monday Exercise 6 15:15-17:00
To be determined
Lab week (week 21)
Changes made since the last occasion
A summary of changes made since the last occasion.
Learning outcomes
Link to the syllabus on Studieportalen.
Examination including compulsory elements
Examination and grading will be based on the solutions to the hand-in problems and performance on the final written examination. The lab report part is graded with pass/fail.
The total score will be calculated from the weighted score of the exam (60%) and the score of the hand-ins (40%). The grade limits are: 40%-59% Grade 3, 60-79% Grade 4 and 80-100% Grade 5.
The written examination will contain questions where you need to calculate the answer. These will be possible to solve if you remember what you did on the hand-ins. There will also be conceptual questions. If you think through the study questions at the end of the lecture notes, this is a good preparation. You are allowed to bring one A4 paper with handwritten notes (both sides).
Course summary:
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