Error Minimisation in Autonomous and Convolutional Quantum Algorithms through Artificial Intelligence Integration in the Context of the Künneth Theorem

Error Minimisation in Autonomous and Convolutional Quantum Algorithms through Artificial Intelligence Integration in the Context of the Künneth Theorem Mehmet Keçeci ORCID : https://orcid.org/0000-0001-9937-9839, İstanbul, Türkiye Received: 27.09.2025 “Article 5 of the series” Abstract: The reliability and efficacy of quantum algorithms—particularly on today’s noise-sensitive Noisy Intermediate-Scale Quantum (NISQ) devices—are intrinsically linked to robust error mitigation strategies and well-defined performance metrics. This work, drawing on pre-doctoral V. technical reports [315, 463, 468, 469] from Gebze Technical University (Kocaeli, Türkiye), entitled Error Minimisation in Autonomous and Convolutional Quantum Algorithms through Artificial Intelligence Integration in the Context of the Künneth Theorem, presents a comparative analysis of several error mitigation techniques, including Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), and Clifford Data Regression (CDR). Experimental and simulation-based investigations demonstrate that the ZNE technique can achieve a substantial reduction in physical error rates—improving them by approximately three orders of magnitude, from ~0.07% down to ~0.0001%—and further reveal that these mitigation methods can be adaptively tuned according to distinct error regimes. The study strongly emphasises that the choice of ansatz architectures employed in quantum circuit optimisation, as well as the physical layout and connectivity of qubits, directly influence observed error rates. In light of these findings, the work proposes autonomous and convolutional intelligent ansatz structures, enhanced with machine learning capabilities and trained on a database of historically successful, low-error circuit instances. The dynamic development and optimisation of such ansätze through artificial intelligence tools are anticipated to play a pivotal role in the proactive management of quantum errors. The results and metrics introduced herein lay a foundational framework for future automated quantum algorithm design strategies, which are intended to be evaluated within more advanced mathematical contexts—including topological error-correcting codes and the Künneth Theorem. Keywords: Künneth Theorem, quantum algorithms, error mitigation, ansatz optimisation, Zero-Noise Extrapolation (ZNE), qubit architecture, machine learning integration, Majorana fermions, JupyterLab, circuit depth, topological codes, autonomy, convolution, artificial intelligence. Note: Citations and numbering are in continuation of the previous article.