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Course Description

LecturerPaolo Muratore-Ginanneschi 
Teaching AssistantBrecht Donvil
Credits10 (grading info)
LanguageEnglish
Master's Programme Theoretical and Computational Methods
Time span4.09.2018 - 14.12.2018
VenueExactum Building
Lecture timetable
  • Tuesdays 10:15 - 12:00, BK106
  • Wednesdays 10:15-12:00, CK107

Exercise sessionWednesday 16:15-18:00, CK107


The course is directed at physics oriented 
students  at advanced undergraduate or graduate level. The course will start with a reminder of fundamental concepts of multi-partite quantum system to then proceed to  provide an introduction to theory of quantum systems interacting with their environment. Emphasis will be given to the study of two level systems (qubit) playing a central role in the development of quantum computing.

Contents

  • probabilistic foundations of quantum mechanics
  • composite systems, entanglement
  • quantum channels alias completely positive maps
  • quantum Markov processes
  • Lindblad equation
  • repeated interaction systems
  • stochastic Schrödinger equation

Requirements

The course requires linear algebra and differential calculus as discussed in the basic courses. Some very basic understanding of probability is needed. Pre-knowledge of elementary quantum mechanics is helpful.

Literature

The following excellent textbooks books contain all material (and much more) which will be discussed in the course:

  1. Nielsen, M. A. and Chuang, I. L.:  Quantum Computation and Quantum Information , Cambridge University Press 2010
  2. Breuer, H.-P., Petruccione, F.:  The Theory of Open Quantum Systems , Oxford University Press, 2002

Detailed Schedule

DayTimePlaceTopic
Tue 4.9.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bFinite dimensional complex vector spaces (14.09)
Wed 5.9.201810:15 - 12:00

Exactum, CK107, Gustaf Hällströmin katu 2b

Spectral theorem (finite dimensional case) (21.09)
Tue 11.9.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bThe postulates of Quantum Mechanics (21.09)
Wed 12.9.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bMixtures, probability and measurement (21.09)
Tue 18.9.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bQuantum probability I: Gleason's theorem (25.09)
Tue 25.9.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bQuantum probability II: Nelson's theorem
Tue 25.9.201816:15 - 18:00Exactum, C124, Gustaf Hällströmin katu 2bContextuality and Kochen-Specker theorem
Wed 26.9.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bEntaglement and Schmidt's decomposition
Tue 2.10.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bPartial trace and purification (11.12)
Wed 3.10.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bIndirect measurement and Krauss representation
Thu 4.10.201814:15-16:00Exactum, C124,  Gustaf Hällströmin katu 2bComplete positivity and Choi's Theorem
Tue 9.10.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bGorini--Kossakowski--Lindblad--Sudarshan equations (08.12)
Tue 16.10.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bBorn's approximation
Wed 17.10.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bMicroscopic derivation of the GKLS equation
Tue 30.10.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2b
Wed 31.10.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2b
Tue 6.11.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bPhenomenological theory of quantum jumps
Wed 7.11.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bExcursus: conditional expectations
Tue 13.11.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bPiecewise deterministic processes (11.12)
Wed 14.11.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bGeneral form of the stochastic Schrödinger equation with jumps
Tue 20.11.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bBrief overview of infinite dimensional Hilbert spaces
Wed 21.11.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bExamples and some apparent mathematical paradoxes
Tue 27.11.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bA very stylized model of electron trap in a nano-device
Wed 28.11.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2b(Non-)exponential decay in Quantum Mechanics
Tue 4.12.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bvan Hove's scaling limit
Wed 5.12.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bEnvironment-induced superselection rules.
Tue 11.12.201810:15 - 12:00Exactum, BK106, Gustaf Hällströmin katu 2bAn elementary decoherence model
Wed 12.12.201810:15 - 12:00Exactum, CK107, Gustaf Hällströmin katu 2bA brief discussion of the EPR 1935 paper

Exercises

Exercise Session 01
Exercise Session 02
Exercise Session 03
Exercise Session 04
Exercise Session 05
Exercise Session 06
Exercise Session 07
Exercise Session 08
Exercise Session 09
Exercise Session 10
Exercise Session 11 





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