Quantum computing (QC) is a field that has witnessed a rapid increase in interest and development over the past few decades since it was theoretically shown that quantum computers can provide an exponential speedup for certain tasks (Deutsch, Jozsa 1992; Grover 1996; Shor 1994). Translating this potential into a practically relevant quantum advantage, however, has proven to be a very challenging endeavor. Nevertheless, the emerging field is considered to have a highly disruptive potential for many domains, for example in machine learning (Schuld, Sinayskiy, Petruccione 2015), chemical simulations (Cao et al. 2019) and optimization (Li et al. 2020), the domain of this work. Due to the fact that optimization problems are of utmost importance also for industrial applications, we investigated a potential advantage of quantum and quantum-inspired technology for the so-called transport robot scheduling problem (TRSP), a real-world use-case in optimization that is derived from an industrial application of an automatized robot in a high-throughput laboratory. The optimization task is to plan a time-efficient schedule for the robot's movements as it transports chemical samples between a rack and multiple machines to conduct experiments.

We consider the problem of computing a sparse binary representation of an image. To be precise, given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors that when added together best reconstruct the given input. We formulate this problem with an $L_2$ loss on the reconstruction error, and an $L_0$ (or, equivalently, an $L_1$) loss on the binary vector enforcing sparsity. This yields a so-called Quadratic Unconstrained Binary Optimization (QUBO) problem, whose solution is generally NP-hard to find. The contribution of this work is twofold. First, the method of unsupervised and unnormalized dictionary feature learning for a desired sparsity level to best match the data is presented. Second, the binary sparse coding problem is then solved on the Loihi 1 neuromorphic chip by the use of stochastic networks of neurons to traverse the non-convex energy landscape. The solutions are benchmarked against the classical heuristic simulated annealing. We demonstrate neuromorphic computing is suitable for sampling low energy solutions of binary sparse coding QUBO models, and although Loihi 1 is capable of sampling very sparse solutions of the QUBO models, there needs to be improvement in the implementation in order to be competitive with simulated annealing.

We developed and compared Constraint Programming (CP) and Quantum Annealing (QA) approaches for rolling stock optimisation considering necessary maintenance tasks. To deal with such problems in CP we investigated specialised pruning rules and implemented them in a global constraint. For the QA approach, we developed quadratic unconstrained binary optimisation (QUBO) models. For testing, we use data sets based on real data from Deutsche Bahn and run the QA approach on real quantum computers from D-Wave. Classical computers are used to run the CP approach as well as tabu search for the QUBO models. We find that both approaches tend at the current development stage of the physical quantum annealers to produce comparable results, with the caveat that QUBO does not always guarantee that the maintenance constraints hold, which we fix by adjusting the QUBO model in preprocessing, based on how close the trains are to a maintenance threshold distance.