A Study of Computational Frameworks for Unconventional Computing via Electromagnetics

As the design of computer chips heavily relies on computer simulations, it is envisioned that numerical modeling will play an increasingly important role in the development of unconventional computing technologies. This thesis studies the computational frameworks related to the development of unconventional computing, including probabilistic computing and quantum computing. The capability of probabilistic computing in solving NP-complete number theory problems is demonstrated. Generalized Helmholtz decomposition is shown as a theoretical basis for quantization of electromagnetic fields via numerical mode decomposition. A 2D demonstration of numerical quantization with finite difference method is presented. A computational framework amenable to integral equation solver is proposed to investigate the scattering effect on momentum-entangled photons from spontaneous parametric downconversion. A generic model to investigate field-matter interaction with nonlinearity is presented.