Quantum stochastic filtering

This paper presents a new paradigm for stochastic filtering by modeling the unified response of a neural lattice using the Schroedinger wave equation. The model is based on a novel concept that a quantum object mediates the collective response of a neural lattice. The model is referred as recurrent quantum neural network (RQNN). The RQNN model has been simulated in two different ways. In one case the potential field of the Schroedinger wave equation is linearly modulated and in the other case the potential field of the Schroedinger wave equation is nonlinearly modulated. It is shown that the proposed quantum stochastic filter can efficiently denoise signals such as DC, sinusoid, amplitude modulated sinusoid and speech signals embedded in very high Gaussian and non-Gaussian noises. Performance of linearly modulated RQNN compares well with traditional techniques such as Kalman filter and wavelet filter. However, preliminary results show that nonlinearly modulated RQNN performs much better when compared with traditional techniques. For example, nonlinearly modulated RQNN model denoises a DC signal 1000 times more accurately in comparison to a traditional Kalman filter. The most important fact is that the proposed quantum stochastic filter does not make any assumption about the shape and nature of the signal and noise when denoising a signal. In a sense, the proposed quantum stochastic filter is a step forward towards intelligent filtering.