This website is no longer updated.

As of 1.10.2022, the Faculty of Physics has been merged into the TUM School of Natural Sciences with the website For more information read Conversion of Websites.

de | en

Quantum Computing with Superconducting Qubits 2: Advanced Topics

Module PH2308

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2022 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2021

Basic Information

PH2308 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Focus Area Experimental Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2308 is Stefan Filipp.

Content, Learning Outcome and Preconditions


Quantum computing is in the middle of the so-called Noisy Intermediate-Scale Quantum (NISQ) computing era that is characterized by the fact that computer architectures do not yet have error correction mechanisms, but first algorithms that finish within the available coherence time can already be tested on real quantum computer prototypes. These algorithms hold the promise to offer a wide variety of applications, such as in quantum chemistry, finance, or logistics. With these prospects, quantum computing enjoys a very high level of media attention, spurred even more by first signs of a quantum advantage on quantum processors with a few dozens of superconducting qubits as well as by publicly available cloud-based quantum computing services. Based on the first part of the course ‘Quantum Computing with superconducting qubits I: Architecture and algorithms’ we will elaborate on superconducting qubits and discuss their operational principle in detail.

This advanced course will address the following topics:

*) Introduction to quantum computing & superconducting qubit architectures (review ‘QC with superconducting qubits – Part 1’)

*) Different types of superconducting qubits (phase qubit, (generalized) flux qubit, fluxonium qubit, …)

*) Design of superconducting quantum circuits

*) Noise and de-coherence, Master-equation description, characterization measurements (Rabi, Ramsey, Spin-Echo, CPMG, …)

*) Multi-qubit systems, entangling gate, Geometric gates

*) (Optimal) control for high-fidelity operations

*) Calibration & Characterization (Error amplification sequences, randomized benchmarking, …)

*) Measurement of qubit (joint & single-shot readout, reset protocols, quantum-limited amplifiers)

*) Hybrid systems (superconducting quantum circuits coupled to atoms, spins, phonons, …)

*) Error correction and error mitigation, bosonic (cat) codes

*) Applications: Quantum Simulation of Spins, Quantum Chemistry, Optimization, Machine Learning

Learning Outcome

After the successful completion of the module you will

*) be knowledgeable about different types of superconducting qubits

*) understand the design principles for superconducting quantum circuits  

*) understand how to model and characterize noise and decoherence

*) understand how to entangle qubits using different types of gates

*) know how to accurately control and readout superconducting qubits

*) understand how microwaves can serve as a quantum link to other systems

*) know about promising applications and current demonstrations of quantum algorithms on superconducting qubit platforms

In the exercise class you will be given problem sets with 2-4 questions per week that will be discussed in the classroom (situation dependent taking place virtually). To complete the exercise class you will be given the opportunity to present a lecture-related topic (on a research paper or on the implementation of an algorithm).


No preconditions in addition to the requirements for the Master’s program in Physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module contains a lecture and an exercise. In the lecture the learning content is presented and discussed. In the exercises the students will get the chance to deepen their understanding with problem examples and calculations as well as programming examples using cloud-based quantum computing services (e.g. IBM Q Experience).


Powerpoint slides, Jupyter/Python notebooks, Videostreams & online discussion groups (situation dependent)


  • Lecture notes (slides)
  • P. Krantz et al. 'A quantum engineer's guide to superconducting qubits'. Applied Physics Reviews 6, 021318 (2019).
  • Nielsen & Chuang, 'Quantum Computation and Quantum Information'. Cambridge Univ. Press.
  • 'Learn Quantum Computation with Qiskit','.
  • Steve Girvin's Les Houche Lecture Notes
  • P. Krantz et al. 'A quantum engineer's guide to superconducting qubits'. Applied Physics Reviews 6, 021318 (2019) (
  • A. Blais et al. ‘Circuit Quantum Electrodynamics’ (
  • M. Kjaergaard, Superconducting Qubits: Current State of Play Annual Review of Condensed Matter Physics: Vol. 11:369-395, (2020) (

Module Exam

Description of exams and course work

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Describe experimental methods to characterize the noise spectral density that affects the coherence of a qubit.
  • Describe the working principle the quantum adiabatic optimization algorithm (QAOA).
  • Describe different methods to entangle superconducting qubit. Explain which one is more suited for quantum chemistry calculations.
  • Derive the Hamiltonian of a flux qubit and explain the difference to a transmon qubit.
  • What are the challenges to compute the groundstate of molecules on a quantum computer using a variational algorithm?

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of presentation of a lecture-related topic in the exercise class

Exam Repetition

The exam may be repeated at the end of the semester.

Top of page