Estudo da viabilidade do uso da computação quântica para análise de propriedades de sólidos periódicos

Abstract

Materials science has been developed over the last few decades with great help from digital simulations on the supercomputers that we have available in the current century. However, there are certainly known limits to how far these simulations can go and which systems we can simulate in an effective computation time. Quantum computing comes with promises to break certain barriers of classical computing, increasing the computing capacity available for the most diverse tasks, and, possibly, one of them will be materials science. In our work, we carried out a bibliographic review of what is currently done for the simulation of periodic materials through quantum computing, as well as we also carried out some simulations on quantum computers available for public access. A major point of our survey was that, among all applications of quantum computing, the application in periodic solid physics is still modest, while the applications on molecules being one of the largest sources of works and references. With that in mind, we were able to perform simulations for the band structure of some atoms, such as silicon and graphene, in a local simulator. We were also able to simulate a generalized Hamiltonian model in a quantum machine in silico, to study its behavior as we varied its parameters. For graphene, we were able to compute its structure in a local simulator and the result was similar to that expected in the literature. For silicon, we obtained a marked difference in its excited energy state, which we believe to be due to the simplicity of our approximation.