The rising energy production costs and the increasing reliance on volatile renewable sources have driven the need for more efficient power system redispatch strategies. In this work, we re-interpret the redispatch problem as a multi-objective combinatorial optimization task within the Quadratic Unconstrained Binary Optimization (QUBO) framework, suitable for adiabatic quantum computing. Our contributions include a novel normalized unbalanced penalty method that integrates inequality constraints via a quadratic Taylor expansion and an$\alpha$-Expansion algorithm that allows us to address largescale redispatch instances and to integrate temporal adjacent state switching constraints directly into the algorithm. Our experiments are conducted on open data of the German power system. Our results, obtained via numerical simulation and from an actual D-Wave Advantage quantum annealer, validate the viability of our formulation and demonstrate that our algorithm scales to large problem instances.

Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum Computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithms which are based on branch-and-cut-and-prize. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulations and state-of-the-art MAPF solvers.

In this work we explore the use of quantum computers in solving the NP-hard placement problem of the Field-Programmable Gate Array (FPGA) implementation phase and introduce a novel approach suited for current quantum hardware sizes. Adiabatic quantum computing (AQC), with its capability to traverse expansive solution spaces, is a good fit for addressing this combinatorial problem with its exponentially large solution space. Instead of solving a single the whole problem at once, we re-formulate the placement problem as a series of so called quadratic unconstrained binary optimization (QUBO) problems which are subsequently solved via AQC. Our novel formulation facilitates a straight-forward integration of design constraints. Moreover, the size of the sub-problems can be conveniently adapted to the available hardware capabilities. Beside the sole proposal of a novel method, we ask whether contemporary quantum hardware is resilient enough to find placements for real-world-sized FPGAs. A numerical evaluation on a D-Wave Advantage 5.4 quantum annealer suggests that the answer is in the affirmative.

Many applications in automated auditing and the analysis and consistency check of financial documents can be formulated in part as the subset sum problem: Given a set of numbers and a target sum, find the subset of numbers that sums up to the target. The problem is NP-hard and classical solving algorithms are therefore not practical to use in many real applications.We tackle the problem as a QUBO (quadratic unconstrained binary optimization) problem and show how gradient descent on Hopfield Networks reliably finds solutions for both artificial and real data. We outline how this algorithm can be applied by adiabatic quantum computers (quantum annealers) and specialized hardware (field programmable gate arrays) for digital annealing and run experiments on quantum annealing hardware.