A Stochastic Filtering Algorithm Using Schrödinger Equation

This paper provides a new adaptive algorithm for single-step prediction by modeling the potential field of a one dimension Schrödinger wave equation using neural network. This new architecture is referred to as the recurrent quantum neural network (RQNN). The RQNN can filter the signal embedded with non-stationary noise without any priori knowledge of the shape of the signal and statistical properties of the noise. We compared the simulation results of the RQNN with a classical adaptive stochastic filter-RLS. It is shown that the RQNN is much more efficient in denoising signals embedded with Gaussian stationary, non-Gaussian stationary and Gaussian non-stationary noise such as DC, sinusoid, staircase and speech signals. The RQNN can enhance the signal to noise rate (SNR) by 20 dB, which is more than 10 dB given by the traditional technology when it denoising sinusoid signal.