Nanoscale Precision-Related Challenges in Classical and Quantum Optimization

Quantum computation and optimization have recently garnered considerable attention, with a noticeable focus on their floating-point and arithmetic designs. In classical computing, numerical optimization problems are commonly employed to assess the performance of optimization algorithms before their application to real-world issues. Nevertheless, precision issues impact the performance analysis of these algorithms, and neglecting these predictable exceptions can lead to unforeseen consequences. Therefore, this study systematically organizes potential precision issues related to how the floating-point storage format impacts optimization. These issues cause the optimal solution to deviate from the theoretical value, introducing imprecision or multiple optimal values, which in turn affects the usability of optimization algorithms, the direction of the search, and the assessment of convergence levels. These analyses offer valuable insights into the practical behavior of optimization algorithms when applied to function optimization problems, aiding researchers in accurately assessing and enhancing algorithm performance. Moreover, these findings contribute to the advancement of both classical and quantum computation.