Quantum Synthetic Models for Entangled Matter Out of Equilibrium

The exceptional features of many-body quantum systems out of equilibrium are intimately connected with the intrinsic limitations we face when simulating their dynamics on a classical computer, as both are a consequence of the fact that quantum matter is entangled. Digital quantum simulators, or quantum computers, promise to overcome these limitations. However, in the current era of Noisy-Intermediate-Scale-Quantum (NISQ) devices, large-scale fault-tolerant quantum computation is out of reach, making full-fledged quantum simulation an ambitious long-term goal. Still, NISQ devices already provide new horizons and opportunities for fundamental research in many-body physics. Indeed, in their native hardware, they can be conceptualized as qubit systems evolving by discrete gates, measurements, and feedback, giving rise to completely new collective behavior and universal phenomena. This project has the ambitious goal of finding and theoretically characterizing new phases of matter which are exclusive to NISQ platforms, charting their largely unexplored phenomenology and possibilities. Taking on a fundamental perspective, at the intersection of many-body physics and quantum information theory, we will pursue this goal based on the study of synthetic models of quantum circuits and quantum cellular automata (QCA). The target results of this project include: (i) Prediction of new dynamical phases arising thanks to the building blocks of NISQ technology and identification of protocols to observe them in existing platforms; (ii) Deeper understanding of topical but hard problems in many-body physics out of equilibrium, made possible by the simplifying minimal structure of quantum-circuit and QCA models. The proposed research is expected to stimulate new synergies between different communities, reflecting the dual nature and interdisciplinary interest of NISQ devices, being both early prototypes for quantum computers and experimental platforms for many-body physics.