Quantum annealing for microstructure equilibration with long-range elastic interactions

We demonstrate the use and benefits of quantum annealing approaches for the determination of equilibrated microstructures in shape memory alloys and other materials with long-range elastic interaction between coherent grains and their different martensite variants and phases. After a one dimensional illustration of the general approach, which requires to formulate the energy of the system in terms of an Ising Hamiltonian, we use distant dependent elastic interactions between grains to predict the variant selection for different transformation eigenstrains. The results and performance of the computations are compared to classical algorithms, demonstrating that the new approach can lead to a significant acceleration of the simulations. Beyond a discretization using simple cuboidal elements, also a direct representation of arbitrary microstructures is possible, allowing fast simulations with currently up to several thousand grains.