Théorique, numérique
Strongly correlated materials are, by definition, materials for which easy classical computational approaches, such as mean-field theory, break down: they are typically unable to explain the exotic quantum phases that these materials display. To explain those phenomena, exponentially costly algorithms (Lanczos method, Monte-Carlo approaches, tensor-network methods) have been developed over the years, but still fail to reach physically interesting regimes due to their cost. Quantum computers have been proposed to circumvent this exponential hurdle: thanks to their quantum properties, they provide, at least on paper, fast (polynomial) algorithms to tackle strongly correlated materials. In reality, however, the levels of noise inherent to current and near-term quantum processors severely challenge the promises of quantum computing. The goal of this internship is to develop algorithmic methods to extend the reach of classical algorithms thanks to quantum algorithms. The approach will be to identify the most promising candidates on both classical and quantum sides and devise hybrid methods that play on their respective strengths. A typical first direction will be the use of (classical) embedding methods such as dynamical mean field theory and solve it using quantum algorithms possibly supplemented with classical algorithms, such as tensor networks or Monte-Carlo algorithms.