Course syllabus

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Course-PM

MCC180 MCC180 Open quantum systems lp4 VT23 (7.5 hp)

The course is offered by the department of Microtechnology and Nanoscience in English.

The lectures take place in Luftbryggan A810 at MC2, if nothing else is communicated.

Contact details

 

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 on 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, with the purpose of complementing the theoretical description with hands-on experience.

Schedule

TimeEdit

Course literature

"The theory of open quantum systems", H.-P. Breuer and F. Petruccione, Oxford University Press

 

Course design

Preliminary  course schedule

Lectures W1 (week 12)
Mon Lecture 1 13:15-15:00
Introduction to Open Quantum Systems
Introduce density matrices
Quantizing Electrical Circuits 1
Hand-out of first hand-in sheet

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 Exercise 1 13:15-15:00
Open Quantum Systems + Quantizing Electrical Circuits

Thursday Lecture 4  10:00-11:45
Quantizing Electrical Circuits 2 (LC + JJ + Transmission)

Friday Lecture 5 15:15-17:00
Quantizing Electrical Circuits 3 (Transmission + Legendre)

Easter (week 14)

Lecture W3 (week 15)
Wednesday Lecture 5 13:15-15:00  Deadline Hand-In 1
Introducing Bloch equations and expressions for T1 and T2

Friday Exercise 2 15:15-17:00 Hand out Hand-in 2
SPAM errors and randomized bench-marking 

Lab session week 16
and Thursday week 15

Lecture W4 (week 17)
Mon Lecture 6 13:15-15:00
Input- and output operators, coherent states and the damped harmonic oscillator

Thursday Lecture 7 08:00-09:45
Quantum Trajectories 1

Thursday Exercise 4 10:00-11:45
Present Hand-In 1 solutions

Lecture W5 (week 18)
Thursday Lecture 8 08:00-09:45
Quantum Trajectories 2
Thursday Lecture 9 10:00-11:45
Input-output formalism 1

Friday Exercise 5  15:15-17:00
Input-output formalism

Lecture W6 (week 19)
Mon Lecture 10 13:15-15:00  Deadline Hand-In 2
Input-output formalism 2
Thursday Lecture 11 08:00-09:45
Weak measurements 1

Thursday Exercise 6 10:00-11:45
Weak measurements

Lecture W7 (week 20)
Mon Lecture 12 13:15-15:00
Weak measurements 1

Lecture W8 (week 21)
Mon Lecture 13 13:15-15:00
(Back-up Q&A)
Thursday Lecture 14 08:00-09:45
(Back-up Q&A)
Thursday Exercise 7 10:00-11:45
(Back-up Q&A)

 

Learning outcomes

* derive the Hamiltonian of the transmon qubit
* derive the Lindblad master equation from a microscopic Hamiltonian
* numerically simulate the dynamics of an open quantum system
* understand what relaxation and dephasing does to a qubit

 

Link to the syllabus on Studieportalen.

Study plan

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%).

Course summary:

Date Details Due