Quantum Computing with Superconducting Qubits 2: Advanced Topics

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

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.

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', https://qiskit.org/textbook/preface.html'.
• 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) (https://arxiv.org/abs/1904.06560)
• A. Blais et al. ‘Circuit Quantum Electrodynamics’ (https://arxiv.org/abs/2005.12667)
• M. Kjaergaard, Superconducting Qubits: Current State of Play Annual Review of Condensed Matter Physics: Vol. 11:369-395, (2020) (https://arxiv.org/abs/1905.13641)

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