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arXiv:2102.11751 · Nature Physics

Probing quantum information propagation with out-of-time-ordered correlators

Jochen Braumüller, Amir H. Karamlou, Yariv Yanay, Bharath Kannan, David K. Kim, Morten Kjærgaard, Alexander J. Melville, Bethany M. Niedzielski, Youngkyu Sung, Antti P. Vepsäläinen, Roni Winik, Jonilyn Yoder, Terry P. Orlando, Simon Gustavsson, Charles Tahan, William D. Oliver

Published Dec 23, 2021• 125 citations
arXivHTMLPDF
DOI
10.1038/s41567-021-01430-w

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Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): each OTOC(k)\mathrm{OTOC}^{(k)}OTOC(k) measures the 2k2k2k-th Fourier component of the phase distribution associated with the singular values of a spatially resolved truncated propagator. This explains the contrasting sensitivities of time-ordered correlators (TOCs) and higher-order OTOCs to causal-cone structure and to chaotic, integrable, or localized dynamics. Based on this understanding, we further generalize higher-order OTOCs by polynomial transformation of the singular values of the spatially resolved truncated propagator. The resultant signal allows us to construct frequency-selective filters, which we call \emph{OTOC spectroscopy}. This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics.
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