Abstract: 

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.