Many-body Chern number from statistical correlations of randomized measurements

• URL: http://arxiv.org/abs/2005.13543v2
• Date: Thu, 11 Feb 2021 19:40:30 GMT
• Title: Many-body Chern number from statistical correlations of randomized measurements
• Authors: Ze-Pei Cian, Hossein Dehghani, Andreas Elben, Beno\^it Vermersch, Guanyu Zhu, Maissam Barkeshli, Peter Zoller, Mohammad Hafezi
• Abstract summary: We propose an ancilla-free experimental scheme for the measurement of the many-body Chern number (MBCN) Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction. Results apply to disk-like geometries that are more amenable to current quantum simulator architectures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant is conventionally based on the linear-response techniques which require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction. Remarkably, our results apply to disk-like geometries that are more amenable to current quantum simulator architectures.

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