Topological Order in Noisy Quantum Systems

Quantum condensed matter has traditionally focused on ground states and equilibrium properties of spatially extended systems, such as electrons in crystalline materials. However, the advent of noisy-intermediate-scale-quantum (NISQ) devices has sparked interest in many-body open quantum systems, where condensed matter meets quantum information. In this talk, I will discuss recent progress in defining phases of matter in open quantum systems and present a partial classification of “intrinsically” mixed-state topological order in terms of non-modular braided fusion categories. I will also discuss an autonomous error correction protocol that leverages erasure errors to stabilise a topological quantum memory in two spatial dimensions, which has been a long-standing quest in the field.