Quantum Optimization ISC 2025

Quantum computing is a rapidly evolving technology with significant potential, particularly for
solving optimization problems. Hard-to-solve classical challenges, such as graph-based problems,
hold high practical relevance. A notable example is task mapping, where quantum approaches
could provide groundbreaking solutions. Currently, hybrid methods such as the Quantum Approx-
imate Optimization Algorithm (QAOA) are especially promising as they circumvent some of the
disadvantages of noisy intermediate-scale quantum computers.
This tutorial has two main parts. The first part is an introduction to quantum computing, which
familiarizes beginners with the concepts and programming of gate-based quantum computers. This
section provides intuitive explanations and beginner-friendly tutorials, ensuring no prior knowledge
of quantum mechanics is required. The Qiskit programming framework will be used in the hands-
on tutorials to deepen the understanding of quantum computing. Quantum simulators will be
used to simulate, analyze, and understand the action of quantum gates and how typical quantum
algorithms are designed.
The second part provides an introduction to solving optimization problems with the QAOA ap-
proach, a quantum algorithm designed for solving combinatorial optimization problems by integrat-
ing gate-based quantum circuits and classical optimization. It will show how the QAOA approach
is rooted in the variational quantum eigensolver framework and how it can leverage parameterized
quantum circuits to tackle NP-hard problems with potential quantum speedups. The interplay
between cost and mixer Hamiltonians and the optimization of circuit parameters will be discussed.
As a practical example, we will focus on a problem well known to many attendees from the field of
HPC, namely mapping tasks to machines. This problem can be generalized to a graph optimization
problem, which has high practical, theoretical and educational relevance and is familiar to most
IT scientists, broadening the appeal of the tutorial. As in our previous successful ISC and SC
tutorials on quantum machine learning we will provide a mixture of presentations and practical
exercises to increase participant engagement.
By the end of this tutorial, participants will have a hands-on understanding of quantum computing,
its challenges, and its potential to revolutionize optimization problems like those encountered in
HPC. In addition, they will gain the ability to identify whether the optimization problems they
encounter might be more efficiently solvable using QAOA.

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Contributors:

• Patrick Gelß
• Aasish Kumar Sharma