The development of numerical analysis techniques for electromagnetics and quantum mechanics problems has dramatically increased the rate of new discoveries.  Propelled by the exponential growth of computers over the past decades, numerical software has brought the ability to reliably experiment with new ideas and predict new phenomena, even before the physical realizations of these ideas in the labs.  This presentation will demonstrate the application of this capability by applying numerical analysis techniques to design and analyze new devices.  First, a system of optical logic gates using a nonlinear metallodielectric grating is completely designed and simulated using numerical analysis.  Second, the Schrödinger equation is numerically solved to calculate the tunneling current for a floating-gate transistor.  Third, numerical techniques are applied to the Schrödinger equation to model quantum gates.  This modeling is validated by comparing simulation results against experimental data that measured transit times for an atom through a potential barrier.  Finally, I will show how to investigate hyperfine and Zeeman interactions as applicable to quantum information processing.