Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned VQC optimization, but are either slow, sample inefficient or require infeasible circuit depth to realize advantages. Quality diversity (QD) search methods combine diversity-driven optimization with user-specified features that offer insight into the optimization quality of circuit solution candidates. However, the choice of quality measures and the representational modeling of the circuits to allow for optimization with the current state-of-the-art QD methods like covariance matrix adaptation (CMA), is currently still an open problem. In this work we introduce a directly matrix-based circuit engineering, that can be readily optimized with QD-CMA methods and evaluate heuristic circuit quality properties like expressivity and gate-diversity as quality measures. We empirically show superior circuit optimization of our QD optimization w.r.t. speed and solution score against a set of robust benchmark algorithms from the literature on a selection of NP-hard combinatorial optimization problems.

Surrogate models are ubiquitously used in industry and academia to efficiently approximate black box functions. As state-of-the-art methods from classical machine learning frequently struggle to solve this problem accurately for the often scarce and noisy data sets in practical applications, investigating novel approaches is of great interest. Motivated by recent theoretical results indicating that quantum neural networks (QNNs) have the potential to outperform their classical analogs in the presence of scarce and noisy data, we benchmark their qualitative performance for this scenario empirically. Our contribution displays the first application-centered approach of using QNNs as surrogate models on higher dimensional, real world data. When compared to a classical artificial neural network with a similar number of parameters, our QNN demonstrates significantly better results for noisy and scarce data, and thus motivates future work to explore this potential quantum advantage. Finally, we demonstrate the performance of current NISQ hardware experimentally and estimate the gate fidelities necessary to replicate our simulation results.

Variational Quantum Algorithms are one of the most promising candidates to yield the first industrially relevant quantum advantage.Being capable of arbitrary function approximation, they are often referred to as Quantum Neural Networks (QNNs) when being used in analog settings as classical Artificial Neural Networks (ANNs).Similar to the early stages of classical machine learning, known schemes for efficient architectures of these networks are scarce.Exploring beyond existing design patterns, we propose a reduced-width circuit ansatz design, which is motivated by recent results gained in the analysis of dropout regularization in QNNs.More precisely, this exploits the insight, that the gates of overparameterized QNNs can be pruned substantially until their expressibility decreases.The results of our case study show, that the proposed design pattern can significantly reduce training time while maintaining the same result quality as the standard "full-width" design in the presence of noise.

A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs).Similar to deep learning, vanishing gradients pose immense problems in the trainability of PQCs, which have been shown to arise from a multitude of sources.One such cause are non-local loss functions, that demand the measurement of a large subset of involved qubits.To facilitate the parameter training for quantum applications using global loss functions, we propose a Sequential Hamiltonian Assembly, which iteratively approximates the loss function using local components.Aiming for a prove of principle, we evaluate our approach using Graph Coloring problem with a Varational Quantum Eigensolver (VQE).Simulation results show, that our approach outperforms conventional parameter training by 29.99% and the empirical state of the art, Layerwise Learning, by 5.12% in the mean accuracy.This paves the way towards locality-aware learning techniques, allowing to evade vanishing gradients for a large class of practically relevant problems.

Anomaly detection in Endpoint Detection and Response (EDR) is a critical task in cybersecurity programs of large companies.With rapidly growing amounts of data and the omnipresence of zero-day attacks, manual and rule-based detection techniques are no longer eligible in practice.While classical machine learning approaches to this problem exist, they frequently show unsatisfactory performance in differentiating malicious from benign anomalies.A promising approach to attain superior generalization than currently employed machine learning techniques are quantum generative models.Allowing for the largest representation of data on available quantum hardware, we investigate Quantum Annealing based Quantum Boltzmann Machines (QBMs) for the given problem.We contribute the first fully unsupervised approach for the problem of anomaly detection using QBMs and evaluate its performance on an EDR inspired synthetic dataset.Our results indicate that QBMs can outperform their classical analog (i.e., Restricted Boltzmann Machines) in terms of result quality and training steps in special cases.When employing Quantum Annealers from D-Wave Systems, we conclude that either more accurate classical simulators or substantially more QPU time is needed to conduct the necessary hyperparameter optimization allowing to replicate our simulation results on quantum hardware.

Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention.However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware, hybrid methods using both classical and quantum machine learning paradigms have been proposed.For instance, transfer learning methods have been shown to be successfully applicable to hybrid image classification tasks.Nevertheless, beneficial circuit architectures still need to be explored.Therefore, tracing the impact of the chosen circuit architecture and parameterization is crucial for the development of beneficially applicable hybrid methods.However, current methods include processes where both parts are trained concurrently, therefore not allowing for a strict separability of classical and quantum impact.Thus, those architectures might produce models that yield a superior prediction accuracy whilst employing the least possible quantum impact.To tackle this issue, we propose Sequential Quantum Enhanced Training (SE-QUENT) an improved architecture and training process for the traceable application of quantum computing methods to hybrid machine learning.Furthermore, we provide formal evidence for the disadvantage of current methods and preliminary experimental results as a proof-of-concept for the applicability of SEQUENT.

In recent years, quantum machine learning has seen a substantial increase in the use of variational quantum circuits (VQCs). VQCs are inspired by artificial neural networks, which achieve extraordinary performance in a wide range of AI tasks as massively parameterized function approximators. VQCs have already demonstrated promising results, for example, in generalization and the requirement for fewer parameters to train, by utilizing the more robust algorithmic toolbox available in quantum computing. A VQCs’ trainable parameters or weights are usually used as angles in rotational gates and current gradient-based training methods do not account for that. We introduce weight re-mapping for VQCs, to unambiguously map the weights to an interval of length 2π, drawing inspiration from traditional ML, where data rescaling, or normalization techniques have demonstrated tremendous benefits in many circumstances. We employ a set of five functions and evaluate them on the Iris and Wine datasets using variational classifiers as an example. Our experiments show that weight re-mapping can improve convergence in all tested settings. Additionally, we were able to demonstrate that weight re-mapping increased test accuracy for the Wine dataset by 10% over using unmodified weights.