A circuit measures how well thermal phases protect quantum information

Ruochen Ma of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, and colleagues have constructed a circuit that can approximately transform one Gibbs state into another provided the two are connected by a path in parameter space along which a certain correlation-decay condition holds. The work extends the established circuit-based characterization of quantum phases from zero-temperature ground states to systems at finite temperatures. For finite-dimensional systems of linear size L, the locality of the circuit is O(log L). This finding establishes a quantifiable relationship between system size and circuit complexity. As an application, the authors show that any system in the same thermal phase as a zero-temperature…