The goal of this thesis is to provide possible solutions to the two issues in silicon photonics. First, I will discuss using topological structures to enhance the transport and nonlinear frequency generation in silicon photonics. We propose a non-periodic photonic system with a structural disorder that confines light near the system boundary, enhancing the nonlinear photon generation rate compared to periodic systems. Next, I will introduce a systematic inverse-design method, aiming to boost the efficiency of on-chip nonlinear photon generation, along with a physical interpretation of these results. Specifically, I will present our experimental demonstration of a compact, robust, and efficient entangled photon pair source based on spontaneous four-wave mixing, achieving a generation rate of 1.1MHz and a coincidence to accidental ratio of 162. This method can also be generalized for other nonlinear optical processes. In the second part of the thesis, I will show the possibility of expanding the optical computing bandwidth with a mode-division multiplexing (MDM) strategy, offering a new degree of freedom in optical computing with the micro-ring resonator platform. I will outline an MDM strategy suitable for small-scale neural networks and a multi-dimensional architectural approach for large-scale optical computing applications. I will present the experimental results of our device for matrix multiplication fabricated at foundry.