The expectations for the fast growing field of quantum computing are high, but up to date a general purpose quantum computer of reasonable size, which can boost materials science modeling, is not yet available. Nevertheless, during the past years a technology known as Quantum Annealing (QA), which is a specific case of adiabatic quantum computing, has emerged and is available with more than 5,000 qubits nowadays. Here we demonstrate that already today this approach can be used for relevant aspects of materials science modeling. In particular, we show how QA can be used for very efficient modeling of stress induced transformations e.g. in large scale shape memory alloys under consideration of long range elastic coherency stresses. The performance of these computations is compared to classical algorithms, leading to a clear acceleration for systems with high numbers of grains. Moreover, we show that QA, which is predominantly designed to identify ground state configurations, can also be used for efficient thermodynamic modeling in the low temperature regime at very low computational cost. Exploiting higher energy states found via quantum annealing, we demonstrate how this new sampling approach can be superior to conventional sampling algorithms for low temperatures.