Quantum computing leverages the unique properties of qubits and quantum parallelism to solve problems intractable for classical systems, offering unparalleled computational potential. However, optimization of quantum circuits remains critical, especially for noisy intermediate-scale quantum (NISQ) devices with limited qubits and high error rates. Genetic algorithms (GAs) provide a promising approach for efficient quantum circuit synthesis by automating optimization tasks. This work examines the impact of various mutation strategies within a GA framework for quantum circuit synthesis. By analyzing how different mutations transform circuits, it identifies strategies that enhance efficiency and performance. Experiments utilized a fitness function emphasizing fidelity, while accounting for circuit depth and T-operations, to optimize circuits with four to six qubits. Our analysis revealed that, while the "swap, addition" strategy achieved the highest fidelity scores, it consistently increased circuit depth. In contrast, combining "swap, addition, delete" strategies offers a more balanced approach, delivering near-optimal results while also having the potential of reducing circuit depth.

We apply a hybrid evolutionary algorithm to minimize the depth of circuits in quantum computing. More specifically, we evaluate two different variants of the algorithm. In the first approach, we combine the evolutionary algorithm with an optimization subroutine to optimize the parameters of the rotation gates present in the quantum circuit. In the second, the algorithm solely relies on evolutionary operations (i.e., mutations and crossover). We approach the problem from two sides: (1) constructing circuits from the ground up by starting with random initializations and (2) initializing individuals with a target circuit in order to optimize it further according to the fitness function. We run experiments on random circuits with 4 and 6 qubits varying in circuit depth. Our results show that the proposed methods are able to significantly reduce the depth of circuits while still retaining a high fidelity to the target state.

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.