Digitized Adiabatic Bayesian Update via Quantum Approximate Optimization Algorithm

We present a gate-based, digitized adiabatic (QAOAstyle) realization of the Bayesian filtering update on discrete grids. Our method encodes the likelihood into a diagonal cost Hamiltonian and implements the anneal via a symmetric Trotter sequence of mixer and cost blocks, avoiding state-conditioned gate constructions and any variational parameter training. We show theoretically that the measurement statistics exhibit the same effective inverse temperature as in the continuous anneal up to O(T3/p2) Trotter error, and that a single energy-scale parameter α (applied only to the cost) restores the target posterior variance after a one-shot calibration. On Gaussian test cases, the calibrated digitized anneal closely matches the analytical posterior while maintaining shallow, structured circuits that scale naturally with the register size. These results position digitized adiabatic filtering as a practical alternative to both analog annealing and state-conditioned gate approaches in quantum data fusion.