Physics - Institute for Condensed Matter Theory Seminar

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Institute for Condensed Matter Theory Seminar: "Symmetry-protected sign problem and magic in quantum phases of matter"

Event Type
Seminar/Symposium
Sponsor
The Physics Department & The Institute for Condensed Matter Theory
Location
via Zoom
Virtual
wifi event
Date
Mar 8, 2021   12:00 pm  
Speaker
Tim Hsieh, Perimeter Institute
Contact
Janice Benner
E-Mail
jbenner@illinois.edu
Views
21

We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively.  We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2XZ2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and symmetry-protected magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and speculate about the greater implications of our results for measurement-based quantum computing.

 

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