  We propose a dynamical matrix product ansatz describing the stochastic
dynamics of two species of particles with excluded-volume interaction and the
quantum mechanics of the associated quantum spin chains respectively. Analyzing
consistency of the time-dependent algebra which is obtained from the action of
the corresponding Markov generator, we obtain sufficient conditions on the
hopping rates for identifing the integrable models. From the dynamical algebra
we construct the quadratic algebra of Zamolodchikov type, associativity of
which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are
obtained directly from the dynamical matrix product ansatz.
