# Introduction to Open Quantum Systems

Schedule | Location | Format | Scope |
---|---|---|---|

Tue. + Thu., 10–12 | B322, Exactum building (Kumpula) | Lecture + Exercise | 10 cr |

The course addresses **physicists and mathematicians** at advanced undergraduate or graduate level. For physics students the course will provide an introduction to theory and examples of quantum systems interacting with their environment. For students of mathematics the course will provide an introduction into to an algebraic treatment of probability and Markov processes.

## Content

- 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. In addition, some very basic understanding of probability is needed. For physicists we recommend some pre-knowledge in quantum mechanics.

## Literature

The main part of the course will rely on the following books:

- Breuer, H.-P., Petruccione, F.:
*The Theory of Open Quantum Systems*, Oxford University Press, 2002 - Wiseman, H. M., Milburn, G. J.:
*Quantum Measurement and Control*, Cambridge University Press, 2009

## Course Organization

Lectures | 06.09.2016–15.12.2016, weeks 36–42 and 44–50 |
---|---|

Exercises | every Tuesday, 09-10, room B321 |

Lecturers | Dmitry Golubev (Aalto), Paolo Muratore-Ginanneschi (Helsinki), Kay Schwieger (Helsinki) |

## Presemo

The course as a dedicated presemo room (web space). To access this web space just follow the foregoing link. Students are encouraged to use the presemo room for any civilized activity pertaining the course.

## Lecture Notes

The lecture notes are grouped not in correspondence to actual lectures but by topics

Lecture 01: The Postulates of Quantum Mechanics | Lecture 11: Completely Positive Semigroups and the Lindblad Equation |

Lecture 02: Probability & Measurements | Lecture 12: Dynamics and the time asymptotic behavior of the evolution operator |

Lecture 03: Dynamics by examples | Lecture 13: van Hove's weak coupling scaling limit |

Lecture 04: Hilbert Spaces, Operators, and Tensor Products | Lecture 14: the Born approximation |

Lecture 05: Subsystems, Commutants, Independence | Lecture 15: the Markov approximation and the Lindbladian |

Lecture 06: Purification, Entanglement | Lecture 16: Linbladian dynamics of the Qubit |

Lecture 07: Jaynes Cummings Hamiltonian I | Lecture 17: Linbladian dynamics of the Caldeira-Leggett model |

Lecture 08: Jaynes Cummings Hamiltonian II | Lecture 18: Quantum jumps |

Lecture 09: Completely Positive Maps, No-Cloning Theorem | Lecture 19: An overview of (Poisson) stochastic differential equations |

Lecture 10: Kraus-Stinespring Representation, Indirect Measurement, Markov Processes | Lecture 20: |

## Exercises

## News

CHANGE OF PLAN:

- On 20.09 we will have exercise session as usual 09-10 (Kay Schwieger) and main lecture 10-12 (Paolo Muratore-Ginanneschi)

- 22, 27, 29.09 lectures will be as follows: 09-11 main lecture (lecturer Kay Schwieger) 11-12 exercises and complements

Starting from the week of Monday 31/10 the exercises are on Tuesdays from 14:15-16:00 in room B119.

## Course feedback

Course feedback can be given at any point during the course. Click here.

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