Dynamical mean field theory algorithms for quantum computers*

We present quantum algorithms to perform calculations for condensed matter systems on currently available quantum computers. Recent developments of noisy intermediate scale quantum (NISQ) computers open a new route for materials simulations that have exponential scaling with system size on classical computers. Quantum embedding approaches, such as dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures and hence remain restricted to small systems, limiting the scope of their applicability. Here we present the Krylov variational quantum algorithm (KVQA) with improved scaling properties, which allows to perform simulations for real material systems on quantum computing emulators (arXiv:2105.13298). We then present a method based on the maximally localised dynamical embedding (MLDE), and show how it allows to reduce the number of qubits required for DMFT simulations (Nature Comp. Sci. 1, 410 (2021)).