Course syllabus

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Course-PM

MCC180 Open quantum systems lp4 VT26 (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

 

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

TimeEdit MCC180 VT26

Course literature

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

Lecture Notes

Notes from exercise sessions: MCC180___Exercise_sessions_260331.pdf

Quantizing electrical circuits:

Lecture notes hand_written

Lecture_notes_Latex

Introduction to Quantum Electromagnetic Circuits by Uri Cool and Michel Devoret

A quantum engineer's guide to superconducting qubits by P. Krantz et al.

Original Transmon qubit paper by J. Koch et al.

Circuit quantization example (with voltage source): The Cooper pair box  

Course design

Preliminary  course schedule

Lectures W1 (week 13)
23/3 Monday Lecture 1 13:15-15:00, Göran
Introduction to Open Quantum Systems
Introduce density matrices

23/3 Monday Tutorial 1 15:15-17:00, Zeidan
Bloch sphere
Lindblad Master equation: relaxation
Tips for assignments

26/3 Thursday Lecture 2 10:00-11:45, Göran
Introducing Lindblad Master equation

27/3 Friday Lecture 3 15:15-17:00 Göran
Introducing Bloch equations and expressions for T1 and T2

Lecture W2 (week 14)
30/3 Monday Lecture 4 13:15-15:00, Thilo
Quantizing Electrical Circuits 1

30/3 Monday Tutorial 2 15:15-17:00, Zeidan
Driven-dissipative qubit
Voltage/current source in circuits

Easter break + re-exams (week 15)

Lecture W3 (week 16)

13/4 Monday Lecture 5  13:15-15:00, Thilo
Quantizing Electrical Circuits 2 (LC + JJ + Transmission)

13/4 Monday Lecture 6  15:15-17:00, Göran
General derivation from weak coupling to a bath

16/4 Thursday Tutorial 3 10:00-11:45, Zeidan
TBA

17/4 Friday Lecture 7 15:15-17:00, Thilo (OBS: This lecture will take place in MC2 Fasrummet!)
Quantizing Electrical Circuits 3 (LC + JJ + Transmission)

Lecture W5 (week 17)

20/4 Monday Lecture 8 13:15-15:00, Göran
SPAM errors and randomized bench-marking 

23/4 Thursday Tutorial 4 10:00-11:45, Zeidan
TBA

24/4 Friday Lecture 9 15:15-17:00, Göran
Input- and output operators, coherent states, and the damped harmonic oscillator

Lecture W6 (week 18)

27/4 Monday Lecture 10 13:15-15:00, Göran
Quantum Trajectories 1

27/4 Monday Tutorial 5 + Lab lecture 15:15-17:00, Zeidan + TBA
TBA

Labs only W7 (week 19)

Lecture W8 (week 20)

11/5 Monday Lecture 11 13:15-15:00, Göran
Quantum Trajectories 2

11/5 Monday Lecture 12 15:15-17:00, Göran
Input-output formalism 1

Lab week (week 21)

18/5 Monday Lecture 13 13:15-15:00, Göran
Input-output formalism 2

18/5 Monday Tutorial 6 15:15-17:00, Zeidan
Weak measurements 1

21/5 Thursday Lecture 14 10:00-11:45, Zeidan
Weak measurements 2

22/5 Friday Lecture 15 15:15-17:00, Göran
TBA

Lecture W10 (week 22)
25/5 Monday Tutorial 7 13:15-15:00, Zeidan
Exam preparation

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 do 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 (75%) and the score of the hand-ins (25%). 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:

Course Summary
Date Details Due