## 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
- Date
- Mar 8, 2021 12:00 pm
- Speaker
- Tim Hsieh, Perimeter Institute
- Contact
- Janice Benner
- jbenner@illinois.edu
- Views
- 7
- Originating Calendar
- Physics - Institute for Condensed Matter Theory Seminar
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.