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In this paper, we study the exact solution of the $q$-deformed $D^{(1)}_3$quantum lattice model with non-diagonal open boundary condition. We demonstratethe crossing symmetry of the transfer matrix and obtain the quantumdeterminant. We construct the independent transfer matrix fusion identities andshow that the fusion processes can be closed. Based on the fusion hierarchiesand polynomial analysis, we obtain the inhomogeneous $T-Q$ relations, exactenergy spectrum and Bethe ansatz equations of the system.

Exact solution of the $q$-deformed $D^{(1)}_3$ vertex model with open boundaries