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These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are immune to local noise. Here, we present a strategy to measure topological invariants on quantum computers. We show that our strategy can be easily integrated with the variational quantum eigensolver (VQE) so that the topological properties of generic quantum many-body states can be characterized on current quantum hardware. We demonstrate the robust nature of the method by measuring topological invariants for both non-interacting and interacting models, and map out interacting quantum phase diagrams on quantum simulators and IBM quantum hardware.<\/jats:p>","DOI":"10.22331\/q-2023-04-27-987","type":"journal-article","created":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T12:03:01Z","timestamp":1682596981000},"page":"987","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":10,"title":["Robust measurement of wave function topology on NISQ quantum computers"],"prefix":"10.22331","volume":"7","author":[{"given":"Xiao","family":"Xiao","sequence":"first","affiliation":[{"name":"Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA"}]},{"given":"J. K.","family":"Freericks","sequence":"additional","affiliation":[{"name":"Department of Physics, Georgetown University, 37th and O Sts. 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