A Quantum Algorithm for the Diffusion Step of Grid-based Filter

Abstract

We propose a simple quantum algorithm for implementing the diffusion step of grid-based Bayesian filters. The method encodes the advected state density and the process noise density into quantum registers and realizes diffusion using a quantum Fourier transform--based adder. This avoids the explicit convolution required in classical implementations and the repeated coin-flip operations used in quantum random walk approaches. Numerical simulations using a gate-based quantum computing simulator confirm that the proposed approach reproduces the desired probability densities while requiring significantly fewer quantum gates and much shallower circuit depth.

This work has been submitted to IFAC for possible publication