Solving optimization problems with a quantum computer

A delivery service must plan its routes to be as fuel-efficient as possible. An electric grid operator must balance generation and consumption to ensure that the grid remains stable. What they have in common is that they are facing optimization problems. Finding the best possible solution among many alternatives is a challenge we encounter in numerous areas of daily life and the economy. Thanks to modern IT applications, many optimization problems can be solved easily today. However, when it comes to very complex problems, even high-performance computers can reach their limits.

Quantum computers can solve certain types of problems much more efficiently than classical computers. As part of the FeedbacQ project, six European research institutions are collaborating to investigate whether optimization problems can also be understood within this context. “We’re making adjustments in several areas,” says Dr. Julian Berberich from the Institute for Systems Theory and Automatic Control at the University of Stuttgart. "We develop methods to translate real-world optimization problems into forms that can be processed by quantum computers. We develop novel quantum algorithms. And we are looking for ways to reduce the error rate of quantum computers. What's new is how we solve these problems – namely, with the help of control theory.”

Quantum computations work fundamentally differently from those of classical computers. Instead of bits, which have a state of either 0 or 1, quantum computers use qubits. These can assume different states at the same time. Quantum algorithms use superpositions and entanglements of these states to amplify certain computational paths and attenuate others. Only the measurement at the end yields a concrete result.

“In FeedbacQ, we are developing a new approach to quantum computing,” says project coordinator Berberich. “We are working on mathematical methods that can be used to monitor quantum algorithms during the computation process and influence them in real time. Using control theory – that is, continuous measurement and readjustment – we aim to enable more reliable, faster, and more resource-efficient calculations.”

The researchers also hope to improve quantum hardware – which is still highly prone to errors – using methods from control theory. They are developing new error-correction techniques that are also based on feedback loops and continuous monitoring and control. Using real-world experiments on quantum computers – including a gate-based device at the Politecnico di Torino – they plan to validate their results and demonstrate their practical significance.

FeedbacQ is led by the University of Stuttgart. The consortium includes Freie Universität Berlin, the Paris-based universities CentraleSupélec and École Nationale Supérieure de Techniques Avancées, the Politecnico di Torino, and the University of Malta.

The three-year project officially kicked off on October 20 with a joint meeting of all partners in Berlin. Scientists from the fields of physics, mathematics, engineering, and computer science will from now on conduct joint research at the intersection of control theory and quantum computing.

The transnational funding network QuantERA is providing 1.15 million euros in support of the project. FeedbacQ prevailed in a highly competitive grant competition: In 2025, 287 projects from 29 countries applied for QuantERA funding, but only 39 were successful.