Quantum Computing with Superconducting Qubits: architecture and algorithms

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. How do quantum computers work? Which algorithms are available that may provide a 'quantum advantage' as compared to their classical counterparts? How can algorithms be optimized so that the underlying quantum hardware is used optimally?  How far advanced is the current technology? And what are the challenges ahead? In this course we want to shed light on these and related question. As one of the most promising platforms for a fully operational quantum computing platform we will elaborate on superconducting qubits and discuss their operational principle in detail. Other promising quantum computing platforms will also be discussed and compared to each other.

The course will address the following topics:

• Basic principles of qubits and quantum gates.
• Basic Algorithms such as Quantum teleportation, Grover's search algorithm, Quantum Fourier Transform or Shor's factorization algorithm.
• Quantum Algorithms for applications (variational algorithms for quantum chemistry, combinatorial optimization problem using quantum approximate optimization algorithm)
• Superconducting quantum circuits for quantum computation (qubits, couplers)
• Control and readout of superconducting qubits.
• Characterization of qubits, gates and quantum processors.
• Overview of other quantum computing platforms such as trapped ions and spin qubits.

After the successful completion of the module you will

• understand the working principles of superconducting qubits.
• understand the operational principles of superconducting qubit-based platforms.
• understand the principles of quantum algorithms and know about promising applications.
• understand how to characterize the quality of a quantum operation and a quantum algorithm.
• be able to program your own quantum algorithms using online available quantum computing platforms (such as the IBM Q Experience).
• understand the challenges ahead for building more powerful quantum processors.
• have a general overview on current quantum computing platforms such as trapped ions and spin qubits and be able to assess the current status and ongoing developments in the field.

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

The module contains a lecture and an exercise both offered in form of a single block module. 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. Quantum algorithms will be programmed using cloud-based quantum computing services (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', https://qiskit.org/textbook/preface.html'.

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 how the coherence time of a superconducting qubit can be measured.
• Describe the working principle of Grover's algorithm.
• Describe a quantum circuit that generates entanglement between two qubits and show that the resulting state is entangled. Describe, how this circuit can be realized with superconducting qubits.
• Write down and explain the Hamiltonian of a Cooper-pair box qubit.
• What are the challenges to compute the groundstate of molecules on a quantum computer using a variational algorithm?