The paper explores the non-invertible symmetry protected topological (SPT) phases in a 1+1d $\mathbb{Z}_2 \times \mathbb{Z}_2$ cluster model. The authors show that the standard cluster Hamiltonian has a non-invertible global symmetry described by the fusion category $\text{Rep}(\text{D}_8)$. This means that the cluster state is not only a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase but also a non-invertible SPT phase. They further identify two commuting Pauli Hamiltonians for the other two $\text{Rep}(\text{D}_8)$ SPT phases on a tensor product Hilbert space of qubits, matching the classification in field theory and mathematics. The edge modes and local projective algebras at the interfaces between these non-invertible SPT phases are also identified. Finally, the authors demonstrate that there does not exist a symmetric entangler that maps between these distinct SPT states, highlighting the unique nature of non-invertible SPT phases.The paper explores the non-invertible symmetry protected topological (SPT) phases in a 1+1d $\mathbb{Z}_2 \times \mathbb{Z}_2$ cluster model. The authors show that the standard cluster Hamiltonian has a non-invertible global symmetry described by the fusion category $\text{Rep}(\text{D}_8)$. This means that the cluster state is not only a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase but also a non-invertible SPT phase. They further identify two commuting Pauli Hamiltonians for the other two $\text{Rep}(\text{D}_8)$ SPT phases on a tensor product Hilbert space of qubits, matching the classification in field theory and mathematics. The edge modes and local projective algebras at the interfaces between these non-invertible SPT phases are also identified. Finally, the authors demonstrate that there does not exist a symmetric entangler that maps between these distinct SPT states, highlighting the unique nature of non-invertible SPT phases.