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QST Experiment: Quantum Hardware

Module PH1009 [QST-EX]

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.

Basic Information

PH1009 is a semester module in English language at Master’s level which is offered in winter semester.

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

  • Mandatory Modules in M.Sc. Quantum Science & Technology

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

Total workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH1009 is Monika Aidelsburger.

Content, Learning Outcome and Preconditions


The PH1009 QST Experiment: Quantum Hardware introduces the students to various different physical implementations of quantum systems. Starting with a brief review of key physical concepts and applications, the module first focuses on light-matter interaction, providing the basic concepts of cavity and circuit quantum electrodynamics (QED) as well as the essential models to describe the quantum systems discussed later. Then, various different experimental approaches to realize superconducting and semiconducting quantum bits are introduced. This includes the techniques for control, manipulation and readout of qubits, the concepts for single and two-qubit gates and the routes to build large quantum processors based on them. In the last part, the foundations of quantum sensing are introduced. This includes the discussion of noise sources and the fundamental limits of sensitivity (standard quantum limit and beyond). Finally, the implementation of quantum sensors via opto-mechanical systems and color centers in semiconductors are discussed. 

Introduction, Overview, Motivation

  • What is “Quantum 1.0”, what is “Quantum 2.0”?

  • Quantum two-level system, quantum harmonic oscillator

  • Superposition, entanglement, relaxation and dephasing (examples NMR, ESR)

  • Quantum vs. classical information

  • Potential applications: computing, simulation, sensing, cryptography

Light-Matter Interaction

  • Light

    • Quantization of electromagnetic field
    • Thermal, coherent, Fock states (photon statistics, correlations, bunching, ...)
    • Photon boxes (mode volume, vacuum field, …)

    • Sources and detectors (optical vs microwave, single photons, coherent light, ..)

    • Entangled photons

  • Matter

    • Natural and artificial atoms, realization of quantum two-level systems

    • Size of dipole moments

  • Light-matter interaction

    • Semi-classical light-matter interaction

    • Jaynes-Cummings model, Rabi model

    • Cavity and circuit electrodynamics (cooperativity, coupling strength, strong vs. ultra-strong coupling)

    • AC Stark effect

  • Experimental tools and methods

Superconducting Quantum Circuits

  • Superconducting resonators (1D vs 3D, quality factor)

  • Superconducting qubits as nonlinear harmonic oscillators (Josephson junction as dissipationless nonlinear inductance)

  • Engineering of Qubit Hamiltonian

    • Interaction strength

    • Anharmonicity

    • Decoherence 

  • Single and two-qubit gates

  • Control, manipulation and readout

Semiconductor Quantum Circuits

  • Resonators

  • Semiconductor quantum bits (III-V quantum dots, donors and defects)

  • Interaction strength, anharmonicity, decoherence & dephasing

  • Single and two-qubit gates

  • Control, manipulation, readout

Atoms/Quantum Gases 

  • Generation and characterization of ultracold quantum gases: experimental techniques (laser cooling and trapping, evaporative cooling)

  • Interactions between ultracold atoms

  • Optical lattices

  • Bose-Hubbard model, Hubbard model

Quantum Sensing 

  • Limitation of sensitivity, noise sources, noise power spectral density, amplifiers

  • Standard quantum limit (SQL) of sensing and measurement

  • Optomechanics 

    • measurement of position using light

    • classical and quantum equations of motion

    • shot noise limit for imprecision noise

    • quantum backaction noise (radiation pressure shot noise limit of optomechanics)

  • Quantum sensing with NV center spin qubits, SQL for sensing with spins

  •  Quantum sensing beyond the SQL: squeezed light or the implementation of quantum non-demolition measurement protocols

Learning Outcome

After completing the Module the student is able to:

  • Understand the physical concepts of quantum science and technology as well as the fundamental techniques for the realization of quantum hardware,

  • Analyze and evaluate specific problems related to the realization of quantum hardware,

  • Design quantum bits and circuits for specific applications,

  • Develop schemes for the control, manipulation and readout of quantum bits and circuits,

  • Understand the concepts of quantum sensing and related hardware implementations based on optomechanical systems and defects in diamond and semiconductors.


No prerequisites beyond the requirements for the Master’s program in Quantum Science and Technology. Familiarity with quantum mechanics is assumed, at the level of an introductory module from a Bachelor’s degree in physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module consists of a lecture series (4 SWS) and exercise classess (2 SWS), comprising two lecture sessions and one exercise session per week. 

Blackboard / tablet PC for the introduction of physical concepts and the quantitative analysis of the effects, beamer projection for the discussion of implementations and the experimentally obtained results, complemented by videos, simulations and selected practical experiments. The students are involved in scientific discussions to stimulate their intellectual power.

In the exercises the content is deepened and applied using examples and calculations. Thus the students are trained to explain and apply the acquired physics knowledge independently.

Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core concepts of the course and for practicing to solve typical exam problems.


Handwritten notes on tablet PC, sketches of experimental setups, presentation of relevant data using PowerPoint, handouts of relevant slides. A pdf document of the lecture content will be provided via the internet for download. At the same time, there will be exercises for download and discussion in exercise groups.


  • Daniel F. Walls, Gerard J. Milburn, Quantum Optics, Springer Verlag.

  • Michael A. Nielsen, ‎Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press.

  • A. M. Zagoskin, Quantum Engineering: Theory and Design of Quantum Coherent Structures, Cambridge University Press.

  • K. K. Likharev: Dynamics of Josephson Junctions and Circuits Gordon and Breach Science Publishers, New York.

  • T. P. Orlando, K. A. Delin: Foundations of Applied Superconductivity, Addison-Wesley, New York.

Module Exam

Description of exams and course work

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.

For example an assignment in the exam might be:

  • How does the Hadamard gate act on the Bloch sphere?
  • What is an example of a map which is positive but not completely positive?
  • What is the Schmidt decomposition, and what is its relevance to entanglement?
  • How can a Schmidt decomposition be found?
  • What is the PPT criterion?
  • What is a purification of a mixed state?
  • How can the state 1/3*|00>+2/3*|11> be converted to a maximally entangled state?
  • Construct a basis of maximally entangled states for two qutrits.
  • Characterize a measurement of an observable in a system of two qubits when restricted to an effective qutrit inside the two-qubit system.
  • Find and characterize a protocol for teleporting an arbitrary two-qubit state.
  • How does the Deutsch algorithm work?
  • Why is the oracle in the Deutsch algorithm not acting as |x> -> |f(x)>?
  • Find a quantum circuit performing a controlled-U two-qubit gate, where U is an arbitrary unitary.
  • What is the idea behind quantum error correction?
  • What happens to continuous errors in quantum error correction?
  • What is the Choi-Jamiolkowski isomorphism?

Exam Repetition

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

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