QuantPhases · From quantum error correcting codes to novel phases of matter in and out of equilibrium

In this action, I propose to extend into new directions the already existing deep connections between quantum error correcting codes and exotic phases of quantum materials. Recent developments in analogue and digital quantum devices call for an extension of our understanding of phases of matter to new regimes, and my project will tackle two such directions: non-Euclidean geometries and dissipative open systems. Both of these are also highly relevant to the quest to develop workable quantum error correcting schemes, which will be crucial to scaling up existing quantum computers.Recent years have seen breakthrough theoretical results in the field of quantum error correction, which utilize spatially non-local connections to outperform previous constructions. I will investigate these from a physical perspective, and use them to develop theories of quantum phases in unusual geometries and the novel phenomena that they host. Doing so will both open up new questions in the field of condensed matter physics and also shed new light on properties of such error correcting codes and help design new ones.Error correction arises from a competition of two different dissipative processes: those that cause the errors and those that are engineered to correct them. Designing better error correction schemes therefore requires a deeper understanding of what qualitatively different behaviors can arise in such dissipative systems and to extend the notion of phases of matter to this context. This will lead to ideas that can both help design better error correcting schemes, while also generalizing to other open quantum systems, relevant for various emerging quantum technologies.During the action I plan to work on these problems under the guidance of a supervisor who has an outstanding track record in the field of theoretical condensed matter physics, with particular expertise in describing dissipative quantum systems.