Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap

Abstract: Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories approaching relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. In this work, we review the state-of-the-art of Tensor Network methods and discuss a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories.