Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies.
We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.
Publisher URL: http://arxiv.org/abs/1801.00999
DOI: arXiv:1801.00999v2
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