Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After completing this course, the student is able to

  • Apply the theoretical framework of quantum mechanics in electric
    circuits and devices, that is, circuit quantum electrodynamics
  • Design and model superconducting quantum circuits: from resonators to qubits
  • Identity electrical circuits of practical interest that behave quantum mechanically
  • Distinguish between linear and non‐linear electronic systems and utilize them for the desired functionalities, for example
  • Hypothesize on the behavior of quantum systems

Credits: 5

Schedule: 01.03.2021 - 12.04.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Jan Goetz, Gheorghe-Sorin Paraoanu

Teacher in charge (applies in this implementation): Jan Goetz, Gheorghe-Sorin Paraoanu

Contact information for the course (valid 10.02.2021-21.12.2112):

Sorin Paraoanu,

Jan Goetz,

Mikko Möttönen,

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    The physical foundations and implementation of solid-state quantum electronics has attracted broad interest in the context of the realization of quantum information processing systems. In this course, we address the physics of superconducting quantum circuits and show how such circuits can be implemented based on superconducting thin films and nanostructures. We discuss the application of superconducting quantum circuits in quantum information processing systems and in quantum simulation. The following specific topics will be addressed:

    • quantization of Josephson junction devices
    • systematic quantization of a network of electric lumped-element components
    • quantum mechanics of 1D transmission lines and resonators
    • cavity–qubit systems
    • operation of superconducting qubits: reset, quantum logic, and readout.

  • Applies in this implementation:

    1.       Lecture 1: Key concepts from
    quantum mechanics and solid-state physics
    . Hilbert space, qubits and
    harmonic oscillators. Quantum mechanics in second quantization formulation.
    Density of states.

    2.       Lecture 2: Components.  Resistors, capacitors, inductors, filters.
    Transmission lines and resonators.

    3.       Lecture 3: Noise in classical and
    quantum electrical circuits
    . Nyquist theorem and the crossover from quantum
    to classical. 

    4.       Lecture 4: Superconductivity and
    the Josephson effect
    . The superconducting order parameter and phase. Tunnel
    barriers and the Josephson effect. Interference and SQUIDs.

    5.       Lecture 5: Introduction to
    simulation and Multiphysics problems using COMSOL
    .  Mathematical preliminaries: a crash course on
    partial differential order equations and boundary value problem; the finite
    element method.  Introduction to
    Multiphysics. COMSOL: A tool for modeling Multiphysics: Walk around COMSOL
    desktop;  COMSOL geometry; COMSOL physics;
    results and post-processing of data.  A real-time
    example: Transmission line and electrostatics.

    6.       Lecture 6: Advanced circuit
    simulations in COMSOL
    Hands-on approach: thermal management, electromagnetism,
    microwave engineering - one model circuit will be discussed in detail.

    7.       Lecture 7: Quantization of
    electrical networks
    . DiVicenzo criteria and how they are related to this
    course. Basic concepts: Lagrangian, Legendre transform to Hamiltonian. Example
    1: harmonic oscillator. Example 2: an-harmonic oscillator. Example 3: harmonic
    oscillator coupled to qubit.

    8.       Lecture 8: Superconducting
    quantum bits
    .  Introducing the transmon
    qubit, the charge qubit, and the flux qubit. Elements of circuit QED: the Rabi
    model and the Jaynes-Cummings model.

    9.       Lecture 9: Single-qubit
    . The transmon: initialization, control and readout. T1 and T2
    measurements. Randomized benchmarking.

    10.   Lecture 10: Architectures for
    2-qubit gates.
      Realization of: iSWAP,
    cPhase, and CNOT. Deep dive: Google’s quantum supremacy experiment.

    11.   Lecture 11: Quantum algorithms.
    Introduction to VQE and Grover search.

    12.   Lecture 12: Challenges in quantum
    . Scaling, the SW-HW gap, and error-correction.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Teaching methods: lectures and exercises 

    Assessment methods: exercises and exam

  • Applies in this implementation:

    Exercises will count as 50%. Feedback from the exercises will be given by the TAs. Exam will count as 50%.

  • Valid 01.08.2020-31.07.2022:

    Lectures: 24 h, exercises: 12 h, exam: 3 h + independent work

  • Applies in this implementation:

    Contact hours: 24h lectures + 12 h exercises. Independent work: maximum 72 h.


Study Material
  • Applies in this implementation:

    The course does not follow a single book or reference. Course materials will be indicated for every lecture.

  • Valid 01.08.2020-31.07.2022:

    Basic knowledge in quantum mechanics including second quantization and harmonic oscillator. Basic knowledge on condensed-matter physics.