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DD2366 Open Quantum Systems 7.5 credits

On the microscopic level, our world is quantum-mechanical, but we ourselves experience it on our level as classical. Until quite recently almost all technology could be understood classically, at least on an intuitive level and in its applications. The reason is that the fundamental quantum-mechanical properties of purity and entanglement so easily disappear when a system interacts with other systems. So it is in most engineered systems. Over the last decades, great progress has nevertheless been made in keeping quantum systems isolated from the environment and in manipulating them from the outside without destroying the quantumness of quantum states. For some specific problems, special-purpose quantum computers with on the order 50-100 qubits can presumably beat any classical computer (the field is developing very quickly, and the progress made must therefore be given the qualifier “presumably”). The course Open Quantum Systems aims to teach the theory which has been developed to describe the evolution of a quantum system interacting with an environment, and outline which consequences follows from this theory for current and future quantum technologies, in particular quantum computing technologies. The course is oriented towards students with a background in Computer Science and/or Electrical Engineering.

Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.


For course offering

Autumn 2024 oquant24 programme students

Application code


Headings with content from the Course syllabus DD2366 (Autumn 2024–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Basic quantum mechanics: Hilbert space, observables, Hermitian operators, the Schrödinger representation, the Heisenberg representation, the interaction representation, the Schrödinger equation, the measurement problem, entanglement, Einstein's 'spooky action at a distance' impact.

Quantum information handling: local operations and classical communication, quantum key distribution, various quantum calculation infrastructures.

Dynamics of open quantum systems in general. Time evolution of partial density matrices. Kraus operators.

Quantum-Markov processes. The Lindblad equation and Lindblad operators.

Decoherence and dissipation. Quality measures.

General dynamics of open quantum systems: The Feynman-Vernon functional.

Real sources of error in quantum calculation components. The Aharonov-Kitaev-Nisan model for error propagation.

The Jaynes-Cumming model and the spin-boson model.

Simulation techniques for open quantum systems with memory.

Intended learning outcomes

After passing the course, the student shall be able to

  • use basic theoretical and numerical methods to describe quantum systems interacting with an environment
  • give an account of how performance and limitations of quantum information systems and components depend on the properties and interference from a quantum mechanical environment
  • evaluate and design quantum information components

in order to

  • in an independent and scientifically substantiated way, be able to understand and appreciate the influence of the environment on mainly quantum information processing systems, but also on quantum technology more generally
  • be able to assess what is possible and not possible to do with a given quantum calculation platform.

Literature and preparations

Specific prerequisites

Knowledge and skills in programming, 6 credits, equivalent to completed course DD1310-DD1319/DD1321/DD1331/DD1337/DD100N/ID1018.

Knowledge in algebra and geometry, 7.5 higher education credits, equivalent to completed course SF1624.

Knowledge in calculus in one variable, 7.5 higher education credits, equivalent to completed course SF1625.

Knowledge in multivariable analysis, 7.5 higher education credits, equivalent to completed course SF1624.

Active participation in a course offering where the final examination is not yet reported in LADOK is considered equivalent to completion of the course. Being registered for a course counts as active participation. The term 'final examination' encompasses both the regular examination and the first re-examination.

Recommended prerequisites

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Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • TEN1 - Written exam, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Grade A is examined through an oral examination.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

Computer Science and Engineering

Education cycle

Second cycle

Add-on studies

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Erik Aurell, e-post:

Transitional regulations

HEM1 is replaced by TEN1.