Eight Bit Quantum Fourier Transform Using the FDTD Method

A way of using the Finite Difference Time Domain method is described to simulate the Quantum Fourier Transform, which is an essential component of Shor's factoring algorithm. This simulation is based on the direct implementation of the time-dependent Schrödinger equation in one dimension. Each bit is simulated as an electron in a harmonic oscillator. The behavior of each quantum gate is simulated by applying a magnetic field in specific orientations for set amounts of time based on the amount of time the electron requires to precess. By using a combination of these quantum gates, it is possible to simulate the behavior of the full Quantum Fourier Transform. An eight bit Quantum Fourier Transform was simulated for this work, but it could easily be expanded to reach higher numbers of bits. Results were compared with computational results and shown to match. Simulations were done in Python without requiring significant computational power.