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Course Description

LecturerPaolo Muratore-Ginanneschi (PMG, UH), Jukka Pekola (JP, Aalto), Bayan Karimi (BK, UH)
Teaching AssistantTuomas Pyhäranta (Aalto)
Credits10 (grading info)
Master's Programme Theoretical and Computational Methods  (UH)
Aalto CodeThe Cooperation on quantum technology education in the Helsinki metropolitan area agreement allows Aalto students to take the course with UH course code
Time span 13.09.2022 - 15.12.2022
VenueOn-site  R001/M234 M3 Aalto and on-line (on-line link TBA)
Web-pageclick here to go to the server
Moodle pageclick here to reach the course MOODLE space
Questionnaire Please fill the form linked here
Lecture timetable
  • Tuesdays 14:15-16:00
  • Thursdays 14:15-16:00

Exercise sessionFridays 10:15-12:00

The course aims at providing basic mathematical and theoretical concepts needed in concrete Quantum Technology applications. The applications in view are those related to concrete experiments performed or ongoing in Aalto laboratories.


  • Stochastic thermodynamics and thermometry
  • GKSL master equation
  • Quantum trajectories


part I Some very basic understanding of probability is needed. Pre-knowledge of elementary quantum mechanics is recommended.


General reference textbooks for the course are

  1. Wiseman, H. M. & Milburn, G. J.: Quantum Measurement and Control Cambridge University Press, 2009.
  2. Breuer, H.-P., Petruccione, F.:  The Theory of Open Quantum Systems , Oxford University Press, 2002.
  3. Jacobs, K.: Quantum Measurement Theory and its Applications Cambridge University Press, 2014.
  4. Barchielli, A. & Gregoratti, M.: Quantum Trajectories and Measurements in Continuous Time, Springer Berlin Heidelberg 2009
  5. Peliti, L. & Pigolotti, S. Stochastic Thermodynamics: a gentle introduction, Princeton University Press 2021.

An alternative source for Open Quantum System are the on-line lectures created by Daria Anttila, Guillermo García-Pérez, Matteo Rossi, Boris Sokolov  and based on a previous publication by Guillermo García-Pérez, Matteo A. C. Rossi, Sabrina Maniscalco. The project uses IBM Q Experience platform for simulating open quantum systems.

"Electron Interference", a scientific movie shot in 1976 which tells about the single electron interference experiment (the most beautiful in physics, according to a poll of the Physics World Journal in 2002). This experiment was performed for the first time in 1974.


The streaming link to the lecture will appear about 15 min before the lecture. For technical reasons link the for the first lecture maybe posted here at very last

DayTimePlace (Aalto)Zoom linkTentative list of topicsLecturer
Tue 13.09.202214:15 - 16:00R001/M234 M3

please use

the link

given in


Classical open systemPMG
Thu 15.09.2022 14:15 - 16:00R001/M234 M3Classical master equations  PMG
Tue 20.09.202214:15 - 16:00R001/M234 M3Work and heat in stochastic thermodynamicsPMG
Thu 22.09.202214:15 - 16:00R001/M234 M3Review of postulates of QMPMG
Tue 27.09.202214:15 - 16:00R001/M234 M3State operator and geometryPMG
Thu 29.09.202214:15 - 16:00R001/M234 M3State operator and geometry (continuation)PMG
Tue 04.10.202214:15 - 16:00R001/M234 M3Elements of Quantum ProbabilityPMG
Thu 06.10.2022 14:15 - 16:00R001/M234 M3Boson and fermion oscillatorsPMG
Tue 11.10.202214:15 - 16:00R001/M234 M3Holomorphic representation of the occupation number dynamicsPMG
Thu 13.10.2022 14:15 - 16:00R001/M234 M3

Jaynes-Cummings-Gaudin model 

Tue 18.10.202214:15 - 16:00R001/M234 M3

Qualitative analysis of unitary time evolution 

Thu 20.10.202214:15 - 16:00R001/M234 M3Master equation for a central oscillatorPMG
Tue 08.11.202214:15 - 16:00R001/M234 M3

Temperature and thermometry

Thu 10.11.202214:15 - 16:00R001/M234 M3
Thermodynamics of tunnel junctionsJP,BK
Tue 15.11.202214:15 - 16:00R001/M234 M3
Thu 17.11.202212:00 - 13:45Zoom
Axiomatic derivation of the completely positive master equationPMG
Thu 17.11.202214:15 - 16:00R001/M234 M3
The Nakajima--Zwanzig projection operator techniquePMG
Tue 22.11.2022 14:15 - 16:00R001/M234 M3
Microscopic derivation of the completely positive master equationPMG
Thu 24.11.202212:00 - 13:45 Zoom
Unraveling of master equations by Poisson processesPMG
Thu 24.11.2022  14:15 - 16:00R001/M234 M3
Stochastic thermodynamics with single electronsJP,BK
Tue 29.11.2022 14:15 - 16:00R001/M234 M3
Quantum heat transport I
Thu 8.12.202212:00 - 13:45 Zoom
General stochastic Schroedinger equation with jumpsPMG
Thu 01.12.202214:15 - 16:00R001/M234 M3
Quantum heat transport II
Thu 8.12.202212:00 - 13:45 Zoom
Quantum trajectories driven by white noisePMG
Thu 8.12.202214:15 - 16:00R001/M234 M3
Open quantum systems IJP,BK
Tue 13.12.202214:15 - 16:00R001/M234 M3
Open quantum systems IIJP,BK
Thu 15.12.202214:15 - 16:00R001/M234 M3
Open quantum systems IIIJP,BK


Link to MOODLE space

DayTimePlace (Aalto)Straeming linkLecturer
Exercise Session 01Fri 23.09.2022 10:15 - 12:00R001/M233 M2link to ZoomTuomas Pyharanta
Exercise Session 02Fri 30.09.2022  10:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 03Fri 07.10.202210:15 - 12:00R001/M233 M2
Tuomas Pyharanta
E3ercise Session 04Fri 14.10.202210:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 05Fri 21.10.2022 10:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 06Fri 04.11.2022 10:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 07Fri 11.11.202210:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 08Fri 18.11.202210:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 09Fri 25.11.202210:15 - 12:00R001/M234 M3
Tuomas Pyharanta
Exercise Session 10Fri 02.12.202210:15 - 12:00R001/M234 M3Quantum heat engines and refrigeratorsJK-KB
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