Applied Quantum Algorithms

This course introduces you the the fascinating field of quantum algorithms and their applications.

The focus of this course is on quantum algorithms that are of practical interest which means that we will not only study the general working principles of these algorithms and their theoretical properties (such as their qubit counts and gate complexity) but also discuss the necessary pre- and post-processing steps (e.g., the encoding of system matrices into quantum-amenable format and the interpretation of probabilistic results) to integrate them into end-to-end quantum-assisted applications. We will, among other topics, discuss state-of-the-art quantum algorithms for solving linear systems of equations, linear and nonlinear differential equations, and continuous as well as combinatorial optimization problems.

The course will cover both quantum annealing and gate-based quantum computing. For the latter we will discuss hybrid quantum-classical algorithms (e.g., variational quantum linear solver (VQLS), quantum alternating operator ansatz (QAOA), and quantum machine learning (QML)) as well as quantum algorithms for fault-tolerance machines (e.g., quantum algorithms for computational fluid dynamics (QCFD)). The course will make use of various simulators that exist for these applications. Depending on time and interest, we might also cover how such simulators work "under the hood" and treat various classical simulation algorithms for quantum circuits such as tensor networks and the stabilizer formalism.

The course will consist of two parts:

- The first part (Q3) will give an introduction into the subject through lectures and hands-on assignments.

- In the second part (Q4) students will work in small teams on individual projects and apply the theory and methods taught in the first part of the course.

As applied quantum computing is an emerging field, the content of the course might eventually change if novel promising approaches appear in recent literature or existing ones are demonstrated to be impractical.