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SK2906 Quantum Circuits 7.5 credits

This course covers some basic concepts in quantum transport and quantum electrical circuits.  We start with normal electrons, looking at tunneling and ballastic transport in electron wave guides.  We then shift to single electron circuits and the Coulomb blockade.  The main part of the course will focus on superconducting circuits.  Starting with the classical nonlinear electrodynamics of superconducting tunnel junctions, we will learn about their microwave properties and how to reveal their quantum nature.  We will discuss how such quantum circuits are used to realize very low-noise microwave amplifiers and we will analyze different designs for superconducting quantum bits.  The challanges of realising a quantum computer with superconducing techoology will be discussed.  Finally, we study circuits that probe the quantum nature of continuum mechanical objects, such as vibrating plates, beams and other micro electro-mechanical oscillators. 

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For course offering

Autumn 2024 Start 28 Oct 2024 programme students

Application code


Headings with content from the Course syllabus SK2906 (Spring 2022–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Basic quantum transport theory: Landauer's formula and Landauer-Biittiker's formalism, coulomb-blocked and single-electron circuits. Basic superconducting electronics: The Josephson effect and classical non-linear dynamics of superconducting circuits. Quantum electrodynamics of superconducting circuits and superconducting quantum bits. Hybrid quantum systems such as quantum optomechanics and quantum acoustics.

Intended learning outcomes

After finished course the student should be able to:

  • apply basic theories of quantum transport
  • formulate and analyze lumped-element model for quantum circuits
  • explain basic concepts of quantum-limited measurement

Literature and preparations

Specific prerequisites

English B / English 6

Completed course SI1146 Vector analysis and Sl1155 Theoretical physics.

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


  • INL1 - Homework Problems, 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.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination



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

Engineering Physics

Education cycle

Second cycle

Add-on studies

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David B Haviland (