1. How far do classical solvers reach, and what can algorithms borrowed from quantum theory add?
   In many application domains one has to make good combinatorial choices among astronomically many available ones. Vehicle routing, scheduling, graph coloring or partioning are typical problems of this kind.
   We address those problems with methods loosely connected to quantum computing that run on ordinary computers and on classical hardware such as Fujitsu's Digital Annealer, an Ising machine.
   We investigate state-of-the-art QUBO solvers (Ising machines), benchmark against strong classical baselines, and identify potential relevant problems that can be recast as QUBO problems.
2. We identify application areas for tensor-network methods in solving differential equations.

Quadratic unconstrained binary optimizations (QUBO) essentially solves Ising ground state problems.
Constraints can be included using penalty terms whose weights decide whether the solver puts more emphasize on meeting the constraints or on finding low-cost solutions.
We develope techniques for finding problem-tailored weights. Moreover, we benchmark our method against strong classical solvers. 

What we work on

• QUBO and Ising formulations of constrained problems, and how to choose penalization weights so that feasible solutions actually win.
• Ising machines, in particular the Fujitsu Digital Annealer, classical special-purpose hardware for Ising and QUBO problems.
• Benchmarking on Max-Cut and related problems against mature classical heuristics and exact solvers.
• Identifying relevant problems that can be recast as QUBO problems: capacitated vehicle routing with time windows (CVRPTW) and optimization tasks in civil engineering.
• Identifying application areas for tensor-network methods in the numerical solution of differential equations (work in progress).

Selected results

• A large-scale benchmark of an Ising machine.
  "A comprehensive benchmark of an Ising machine on the Max-Cut problem". [arXiv:2507.22117]New J. Phys. (2026)
• Penalty weights that scale.
  "Scalable Determination of Penalization Weights for Constrained Optimizations on Approximate Solvers". [arXiv:2604.02416], preprint
• Vehicle routing with QUBO subroutines and learned components.
  "A Hybrid Quantum-Inspired and Deep Learning Approach for the Capacitated Vehicle Routing Problem with Time Windows". conference paper at LION 19, Prague, June 2025 · LNCS 15745, 113–128, Springer (2026), [doi:10.1007/978-3-032-09192-5_8]
• First ideas on where quantum methods could help in civil engineering.
  "Quantum and quantum-inspired computing in civil engineering" · Advanced Engineering Informatics 69, 103960 (2026), [doi:10.1016/j.aei.2025.103960]

Tensor networks for differential equations

We are identifying application areas for tensor-network methods in the numerical solution of differential equations.

Collaboration with Fujitsu

We collaborate with Fujitsu on two fronts: the Digital Annealer (Fujitsu's classical special-purpose hardware for Ising and QUBO problems) and quantum computing more broadly.
The collaboration gives us access to a production-grade Ising machine and to industrially relevant problem instances, and it shapes how we benchmark: against the solvers a company would otherwise use, not against strawmen.