Condensed Matter Seminar: Tyler Ellison, University of Washington, “Symmetry-protected sign problem and magic in quantum phases of matter”

The concept of entanglement is central to the modern study of quantum phases of matter. However, entanglement by itself is insufficient for fully characterizing the complexity of quantum states. In this talk, I will describe two diagnostics for the complexity of a state that go beyond entanglement, and use them to characterize the quantum information-theoretic properties inherent to symmetry-protected topological (SPT) phases. In particular, I will show that certain SPT phases possess an essential resource for universal quantum computation known in the quantum information community as ‘magic’. Second, I will demonstrate that SPT phases have a “symmetry-protected” sign problem – implying that there is a particular obstacle to Monte Carlo simulations. This initiates the study of magic in quantum phases of matter and provides the first analytic demonstration of a sign problem in the amplitudes of a wave function.
This talk is based on arXiv:2010.13803,  and is work done in collaboration with Kohtaro Kato, Zi-Wen Liu, and Timothy H. Hsieh.