Circuit-based chatacterization of finite-temperature quantum phases and self-correcting quantum memory

In many-body physics, quantum phases of matter can be defined as equivalence classes under local unitary transformations: two ground states are in the same phase if they can be transformed into each other by a local unitary circuit. In this talk, I will discuss how to extend this circuit-based characterization of phases to open systems, in particular finite-temperature systems in thermal equilibrium described by Gibbs states. We construct a local quantum channel circuit that approximately maps one Gibbs state to another, provided the two are connected by a path in parameter space along which a certain correlation-decay condition holds. As an application, we show that any system in the same thermal phase as a zero-temperature topological code coherently preserves quantum information for a macroscopically long time, establishing self-correction as a universal property of thermal phases.