Fraunhofer-GesellschaftMathematical optimization methods are used in many industrial applications, such as logistics, mobility, and manufacturing. In the long term, quantum computing offers the potential to reduce the time required to find an optimal solution. Using currently available quantum hardware, research is being conducted in the short and medium term on the use of quantum algorithmic heuristics—for example, to improve solution quality compared to classical heuristics.
For example, at the Fraunhofer Institute for Integrated Circuits IIS, researchers are working on a hybrid quantum-classical algorithm to solve routing problems as part of a subproject of the Bavarian hub of the Fraunhofer Quantum Computing Competence Network BayQS (Bavarian Competence Center for Quantum Security and Data Science).
For the Maritime Inventory Routing Problem (MIRP), the Fraunhofer Center for Maritime Logistics and Services CML has built a demonstrator as part of the IQHH project that compares classical solutions with solutions using a quantum annealer. The methods are compared in terms of solution quality and required runtime. Such benchmarking allows the Fraunhofer Society to increase its visibility within the industry and to be perceived as a competent and objective point of contact in the field of quantum computing.
In the field of optimization, the Applied Systems Engineering (AST) division of Fraunhofer IOSB-AST specializes in solving problems in the energy sector using QAOA. One of the use cases is bidirectional charging of electric vehicles. This focuses on optimizing the charging and discharging processes to meet both user needs and the requirements of the power grid. This approach makes it possible to schedule charging times to coincide with periods of low grid load and high availability of renewable energy, while also allowing energy to be fed back into the grid from vehicle batteries to balance peak loads. This method enables the sustainable and efficient integration of electric vehicles into the energy system, offering both economic and environmental benefits. The algorithms use qudits to harness the maximum power of current quantum computers. As an add-on to QAOA, the Fraunhofer IOSB-AST is also developing approaches for stochastic and robust optimization. Stochastic optimization allows uncertainties—such as those in PV production forecasts—to be incorporated into the optimization process. Robust optimization minimizes the impact of uncertainties in the optimization models. This involves the use of uncertainty sets to ensure that the solutions remain robust across a wide range of scenarios.
To analyze the algorithms it has developed, Fraunhofer IOSB-AST is investigating tensor networks. The goal here is to gain insights, particularly regarding optimization approaches (such as qubits and qudits). In this process, the quantum algorithms are compared with the corresponding quantum-inspired algorithms. To gain a comprehensive understanding, Fraunhofer IOSB-AST has developed its own tensor network library in Python.
At the Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS, researchers examine various types of combinatorial optimization problems that originate in artificial intelligence or industrial applications. In addition to problem modeling, general methods for solving a wide variety of combinatorial optimization problems using quantum computing are developed and applied. As part of this effort, a quantum-inspired digital annealer was developed. The chip enables the solution of quadratic optimization problems, which are also used in quantum annealers or QAOAs. It can solve problems with 2,048 variables under full connectivity, which significantly exceeds the current capabilities of quantum annealers and gate-based quantum computers. The hardware has a low power consumption of less than 10 W and does not require a classical server for control, enabling its use on-premises or in resource-constrained environments.
In addition, Fraunhofer IAIS has developed methods for automatically reformulating quadratic optimization problems in a way that demonstrably improves their solvability on quantum hardware. Finally, Fraunhofer IAIS presented a novel quantum circuit that has been proven to solve certain quadratic problems faster than classical hardware. These techniques were developed as part of research projects, including the Lamarr Institute for Machine Learning and Artificial Intelligence, and have been successfully deployed by industry partners, including the Thales Group and PricewaterhouseCoopers International.
At Fraunhofer IGD, ZAQC investigates quantum and quantum-inspired approaches for solving complex optimization problems and benchmarks them against classical methods. One application example is the use of quantum annealing for protein folding to assess the potential of current and future quantum hardware for large search and optimization spaces.
The Fraunhofer Institute for Industrial and Economic Mathematics ITWM, with its own optimization division and a wide range of optimization-related use cases, has a strong interest in the further development of quantum optimization algorithms. In the EnerQuant project, the focus was on modeling and solving an optimization problem in the energy sector. Here, a new, more efficient QUBO model was developed that allows us to specify suitable penalty factors for the constraint penalty terms a priori. Additionally, these factors are optimized using iterative methods to achieve better results for medium-sized problem instances. Furthermore, initial methods for solving robust optimization problems with uncertain parameters were presented. The QuSAA project focuses on portfolio optimization. In addition to efficient modeling of new objective functions—such as the Solvency Capital Ratio (SCR)—expertise in solving multi-criteria optimization problems was developed, and the existing variational algorithm was improved. Additional expertise in optimization was developed in the SQEDULE project. The institute’s goal is to further develop (hybrid) quantum optimization methods using classical optimization tools (e.g., decomposition or branching methods).
To characterize the limitations of existing quantum computers, numerous benchmarks have been proposed at the component and system levels. However, due to the complexity of errors in quantum systems, these benchmarks do not offer predictive power that extends beyond simple quantum circuits and small-scale examples. Application-oriented benchmarks have been proposed to address this problem, but both results from real quantum systems and use cases that go beyond contrived academic examples remain very rare.
The Fraunhofer Institute for Industrial Engineering IAO is making a key contribution with a systematic series of examples from real-world applications, such as optimizing loading plans for electric vehicles or optimizing truck routes. These were run on various processors of IBM’s gate-based quantum computers as well as on D-Wave’s Quantum Annealer using the variational quantum algorithms Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigenvalue Solver (VQE), and Quantum Annealing (QA). This research was also implemented in demonstrators as part of the SEQUOIA End-to-End project.