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Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite these progresses, challenges persist due to system noise, errors, and decoherence. These system noises complicate the simulation of quantum systems. The depolarization channel is a standard tool for simulating a quantum system’s noise. However, modeling such noise for practical applications is computationally expensive when we have limited hardware resources, as is the case in the NISQ era. This work proposes a modified representation for a single-qubit depolarization channel. Our modified channel uses two Kraus operators based only on X and Z Pauli matrices. Our approach reduces the computational complexity from six to four matrix multiplications per channel execution. Experiments on a Quantum Machine Learning (QML) model on the Iris dataset across various circuit depths and depolarization rates validate that our approach maintains the model’s accuracy while improving efficiency. This simplified noise model enables more scalable simulations of quantum circuits under depolarization, advancing capabilities in the NISQ era. 

Motivated by the growing threat of distributed denial-of-service (DDoS) attacks and the emergence of quantum computing, this study introduces a novel “quanvolutional autoencoder” architecture for learning representations. The architecture leverages the computational advantages of quantum mechanics to improve upon traditional machine learning techniques. Specifically, the quanvolutional autoencoder employs randomized quantum circuits to analyze time-series data from DDoS attacks, offering a robust alternative to classical convolutional neural networks. Experimental results suggest that the quanvolutional autoencoder performs similarly to classical models in visualizing and learning from DDoS hive plots and leads to faster convergence and learning stability. These findings suggest that quantum machine learning holds significant promise for advancing data analysis and visualization in cybersecurity. The study highlights the need for further research in this fast-growing field, particularly for unsupervised anomaly detection.