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.

Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we transfer and adapt the well-established concept of Shapley values to the quantum realm. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.

In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higherquality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark datasets. We observe competitive performance.

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. We describe how tree inductions and the prediction of class labels of query data can be integrated into this framework. An on-demand sampling method enables predictions with a constant number of classical memory slots, independent of the tree depth. We experimentally study our approach using both a quantum computing simulator and actual IBM quantum hardware. To our knowledge, this is the first realization of a decision tree classifier on a quantum device.

In many supervised learning applications, it is not sufficient to know the most probable class y for a certain data point x. Instead, a well-calibrated probabilistic prediction p(y x) is required. For instance, in clinical applications, class probabilities are important for confidence in model predictions (Challis et al., 2015). Some classifiers intrinsically provide such a posterior probability, e. g. logistic regression or Gaussian process classification (GPC) as described in Rasmussen and Williams (2006). There are also various methods to install or improve such a calibration for a given classification approach (Niculescu-Mizil and Caruana, 2005), like Platt scaling (Platt, 2000) or isotonic regression (Zadrozny and Elkan, 2002).

We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightforward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.

The optimization of production processes can benefit from machine learning methods that incorporate domain knowledge and data from numerical simulations [1]. Typically, such methods aim to model relations between process parameters and the resulting product. In this manuscript, we consider an example from the field of deep drawing, a sheet metal forming process in which a sheet metal blank is drawn into a forming die by mechanical action. Specifically, we study the prediction of product geometries in a cup drawing process based on data from finite element simulations [2].

We address a non-unique parameter fitting problem in the context of material science. In particular, we propose to resolve ambiguities in parameter space by augmenting a black-box artificial neural network (ANN) model with two different levels of expert knowledge and benchmark them against a pure black-box model.