Laminated composite materials allow for the design of light-weight and durable large structures, due to their high specific strength and their tailorable anisotropic stiffness properties. However, finding a stacking sequence that meets specific strength requirements poses a challenging combinatorial optimization problem. To reduce the complexity of the problem, a bi-level approach employs lamination parameters, which encode the stiffness matrix of the laminate. This approach first optimizes for the desired stiffness properties, and then seeks a stacking sequence that approximates the lamination parameters. Despite its concise formulation, the second step remains a difficult task, due to the vast number of possible stacking sequences and additional manufacturing constraints. Genetic algorithms, branch-and-bound methods, and layer-wise optimization are commonly used to address the stacking sequence retrieval problem. In the future, the development of quantum computers could offer promising new approaches to solve this problem. This work outlines how the stacking sequence retrieval problem can be formulated to be generally suitable for quantum algorithms. In this work, we present stacking sequences of a laminate as states in a quantum lattice model. We then construct the Hamiltonian, which captures the optimization problem's loss function. Further, we demonstrate how certain manufacturing constraints, such as the disorientation constraint, can be interpreted as nearest-neighbor interactions, which are incorporated into the Hamiltonian as penalties. As a proof of concept, we conduct numerical simulations of an algorithm that uses the developed Hamiltonian to find solutions to the stacking sequence retrieval problem. Given that due to their limited size, current quantum computers can only handle small versions of the problem, we instead opt to employ a classical tensor network algorithm commonly used for solving quantum lattice models, the density matrix renormalization group (DMRG) algorithm. To achieve this, we deconstruct the Hamiltonian into a matrix product operator.