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In this 46-minute lecture, Tibor Rakovszky explores bottlenecks in quantum channels and defines quantum spin glass order as part of the Thematic Programme on "Entanglement in Many-body Quantum Matter" at the Erwin Schrödinger International Institute. Learn about the proven analogue of the "bottleneck theorem" for Markovian quantum channels, demonstrating how regions of Hilbert space separated by low-weight barriers in a channel's steady state result in prolonged state confinement. Discover how this establishes a lower bound on mixing time using the "quantum bottleneck ratio" concept, which incorporates both diagonal and off-diagonal matrix elements of steady state density matrices. Examine how this theorem provides a dynamic perspective on phases of matter through Gibbs state decomposition, leading to the definition of "topological quantum spin glass" (TQSG) order—a hybrid of classical spin glass models and topologically ordered systems. Follow the proof that TQSG order manifests at low temperatures in quantum low-density parity check codes defined on expander graphs.
