Far-Away-from-eQuilibrium QANTUm Matter in 2D

Understanding the dynamics of quantum matter far from equilibrium is both challenging and has crucial implications for various fields, including statistical mechanics, condensed matter, high-energy physics, and quantum information theory. The difficulty arises from the prohibitive cost of classical simulations and the limited availability of analytical tools. This understanding is not only fundamental for quantum phenomena but also essential for advancing cutting-edge quantum computing technologies, a key global priority identified in the Horizon Europe Work Programme. While recent progress has been made in understanding one-dimensional interacting systems, the dynamics of quantum systems in two dimensions remain poorly understood. Strong indicators, such as the emergence of anyons, suggest that dynamics in two dimensions can be fundamentally different. This project, FAQ-QuantuM2D: Far-Away-from-eQuilibrium QANTUm Matter in 2 Dimensions, aims to advance the state of the art by leveraging a combination of analytical and numerical approaches. The project focuses on local quantum circuits, which are minimal models for many-body quantum dynamics that have led to groundbreaking analytical insights in recent years. Moreover, they are native to quantum computing applications. The proposal will advance our understanding of far-from-equilibrium dynamics and emerging dynamical phases of quantum matter through three specific scientific objectives: understanding localized and ergodic dynamical phases in 2D kinetically constrained models, understanding 2D strongly localized phases, and uncovering novel non-equilibrium dynamics unique to 2D systems. FAQ-QuantuM2D will deepen our understanding of quantum dynamics, yielding significant insights for fields focused on quantum dynamics and quantum technologies. Concretely for the latter, the results can be used for benchmarking quantum computers and finding suitable, classically hard, tasks for them.