QST Experiment: Quantum Hardware

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

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.

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.

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:

• What is the definition of pure and mixed quantum states?
• What do we understand about quantum superposition and entanglement? Can you write down a typical example of an entangled state?
• What are the basic properties of thermal, coherent and Fock states of the light field? How can we generate such states?
• What determines the vacuum field of an electromagnetic resonator?
• What determines the coupling strength between a quantum two-level system and the quantized modes of an electromagnetic resonator?
• What is the difference between weak, strong and ultrastrong coupling? What is the definition of cooperativity?
• What kind of superconducting qubits do you know? What are the key advantages and disadvantages of those qubits?
• How can we realize a spin-photon interface in semiconductor quantum circuits?
• Which physical processes limit the resolution of sensors? What do we understand about quantum limited resolution?
• What is the standard quantum limit (SQL) of sensing and measurement? How can we overcome the SQL?
• What are the physical and technical ingredients for quantum sensing with NV center spin qubits?

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 both exam period directly following the lecture period and subject to the condition that the student passes the mid-term of passing at least 50% of the exercises.