As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters, which is typically the second phase in a common bi-level optimization procedure for minimizing the weight of composite structures. To adapt stacking sequence retrieval for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed numerical state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For the DMRG algorithm, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.

SnSe is a promising thermoelectric material due to its low toxicity, low thermal conductivity, and multiple valence band structures, which are ideal for high electronic transport properties. The multiple valence band structure has attracted many attempts to engineer the carrier concentration of the SnSe via doping, to place its fermi level at a position where the maximum number of valence bands can participate in the electronic transport. Up until now, ~5 × 10¹⁹ cm^-3 was the highest carrier concentration achieved in SnSe via doping. Recently, introducing SnSe₂ into SnSe was found to effectively increase the carrier concentration as high as ~6.5 × 10¹⁹ cm^-3 (at 300 K) due to the generated Sn vacancies. This high carrier concentration at 300 K, combined with the reduction in lattice thermal conductivity due to SnSe₂ micro-domains formed within the SnSe lattice, improved the thermoelectric performance (zT) of SnSe – xSnSe₂ as high as ~2.2 at 773 K. Here, we analyzed the changes in the electronic band parameters of SnSe as a function of temperature with varying SnSe₂ content using the Single Parabolic Band (SPB) model. According to the SPB model, the calculated density-of-states effective mass and the fermi level are changed with temperature in such a way that the Hall carrier concentration (n_H) of the SnSe – xSnSe₂ samples at 773 K coincides with the optimum n_H where the theoretically maximum zT is predicted. To optimize the n_H at high temperatures for the highest zT, it is essential to tune the 300 K n_H and the rate of n_H change with increasing temperature via doping.

In the past decades, Zirconia (ZrO₂) has emerged as a promising technical ceramic, both as high temperature structural material and electrolyte for fuel cells, etc. The traditional synthesis of ZrO₂ with spark plasma sintering (SPS) usually requires a sintering temperature as high as 1200 °C. General interest in lowering the sintering temperature to reduce energy consumption and thermal stresses has led to research on two promising routes – cold sintering via temperature-dependent chemical reactivity and sintering aids, which facilitates mass transport and improves densification. Here we combine both by developing a single-step sintering process benefitting from both water vapor through the in-situ conversion of Zr(OH)₄ to ZrO₂ and liquid phase Bi₂O₃ as a sintering aid. The resultant ZrO₂ has a relative density above 80% with a sintering temperature as low as 900 °C, significantly higher than that of ZrO₂ without sintering aids, which had a relative density of 54%, both sintered at 50 MPa. The dependence of porosity of sintered samples as a function of sintering pressure (range: 50 MPa–300 MPa) and temperature (range 400 °C–1200 °C) is mapped out as guidance for further material property design. A linear relationship between hardness and relative density was found, with a maximal hardness of 6.6 GPa achieved in samples with 30% porosity. In addition to sintered density, phase stabilization of tetragonal ZrO₂ is enhanced at sintering temperature of 900 °C with water vapor and Bi₂O₃, respectively.