# Simulation Methods for Quantum Many-Body Systems

While quantum many-body systems in thermal equilibrium have been extensively investigated using the methodology of statistical mechanics, the theoretical description of quantum many-body systems out of equilibrium remains challenging. The recent development of various experimental platforms including superconducting circuits, ultra-cold atoms, ion traps, and exciton polaritons has enabled the exploration of many-particle systems in non-equilibrium scenarios such as quantum systems prepared in excited states as well as open quantum systems which are externally driven and interact with their environment. This has triggered extensive research activity on quantum simulations.

We study the dynamics of non-equilibrium quantum many-body systems using Matrix Product State techniques as well as the Consistent Mori Projector approach developed by ourselves [P. Degenfeld-Schonburg, M. J. Hartmann, Phys. Rev. B 89, 245108 (2014)].

We develop pioneering machine-learning tools for the simulation of open many-body systems based on variational neural-network ansätze, which can accurately describe the system dynamics with less computer power than more established numerical methods [M. J. Hartmann and G. Carleo, Phys. Rev. Lett. 122, 250502 (2019)].

A prominent example of an open many-body quantum system is a quantum computer consisting of many qubits interacting with each other and their environment. Quantum computers are currently approaching numbers of qubits and gate counts, for which the benchmarking of their performance becomes challenging. We exploit numerical methods described above to simulate and benchmark quantum computing hardware with focus on the development of quantum algorithms and next-generation quantum computers.