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Many-body topological invariants from randomized measurements in synthetic quantum matter

TitleMany-body topological invariants from randomized measurements in synthetic quantum matter
Publication TypeJournal Article
Year of Publication2020
AuthorsA. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, and B\^ıt. Vermersch
JournalScience Advances
Volume6
Abstract

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

URLhttps://advances.sciencemag.org/content/6/15/eaaz3666
DOI10.1126/sciadv.aaz3666