Unconventional computing paradigm methods with application to computational chemistry

Over the last two decades, applied chemistry has experienced a significant shift, integrating theory and modeling as essential aspects of the discipline. This transformation has been driven by advancements in methodology, numerical techniques, and the increased capabilities of computer hardware and software. Notably, parallel Graphics Processing Units (GPUs) have become instrumental in computational chemistry, allowing for efficient simulations alongside traditional CPU-based computing. However, despite these advances, classical computing faces limitations, particularly in solving complex optimization and sampling problems inherent in computational chemistry. These challenges have prompted exploration into alternative computing paradigms, including quantum computing and memcomputing. Quantum computers leverage principles of quantum mechanics to surpass classical computing limits for specific tasks, while memcomputing exploits classical mechanics in a non-Turing manner, using the evolution of physical systems for computation. This thesis examines these alternative paradigms and their potential to address the limitations of classical computing in computational chemistry. It delves into the physical implementations of quantum and memcomputing systems and evaluates their performance through benchmarking against classical methods. Tests include assessing quantum amplitude estimation methods on trapped ion computers, evaluating quantum optimization for crystal structure prediction, and analyzing the effectiveness of memcomputing and adiabatic quantum computing on NP-hard optimization problems. While the results show promise for these alternative paradigms, they also highlight current limitations in hardware and implementation. Nonetheless, the findings suggest a hopeful outlook for the future development and application of quantum computing and memcomputing in computational chemistry.