Quantum Annealing Approaches to Breaking Rsa Encryption

Objective: to study the transformational potential of quantum annealing in solving the problem of simple factorization. Research method(s): the approach includes a comprehensive review of recent experimental breakthroughs and theoretical innovations. In particular, we analyze techniques such as surface code memory, HUBO and QUBO formulations, range-dependent Hamiltonian algorithms, modular locally structured embedding methods, and a modified multiplication table method random number. Research Output(s): the study evaluates the application of quantum annealing to factorization of primes, showing that advanced problem mapping techniques, such as the HUBO and QUBO formulations, significantly improve the efficiency of representing complex factorization problems on quantum hardware. Notably, the inclusion of surface code memory increases the stability of qubit states during annealing, reducing errors and improving computational accuracy It also demonstrates that Hamiltonian's range-dependent algorithms and modular, locally structured embedding methods help optimize qubit interaction, enabling a more accurate factorization process. A modified multiplication table method is presented, providing an optimized computational strategy, especially effective for large composite numbers. Preliminary experiments with random numbers confirm the theoretical conclusions, indicating that these integrated methods allow for better performance than traditional approaches. Taken together, the results highlight the potential of quantum annealing as a solid foundation for solving complex cryptographic problems and lay the foundation for future research into scalable quantum algorithms and hardware implementations. Scientific novelty: the work combines several advanced quantum annealing techniques for factorization of prime numbers, combining experimental innovations with theoretical developments to propose a new framework that improves the efficiency of cryptographic computing.