{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T01:51:17Z","timestamp":1776822677767,"version":"3.51.2"},"reference-count":60,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T00:00:00Z","timestamp":1772668800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"U.S. Department of Energy Office of Science, Science Undergraduate Laboratory Internships","award":["DE-AC02-07CH11358"],"award-info":[{"award-number":["DE-AC02-07CH11358"]}]},{"name":"National Science Foundation","award":["DMR-2143635"],"award-info":[{"award-number":["DMR-2143635"]}]},{"name":"National Science Foundation","award":["DMR-2611305"],"award-info":[{"award-number":["DMR-2611305"]}]},{"name":"National Science Foundation","award":["DMR-2238895"],"award-info":[{"award-number":["DMR-2238895"]}]},{"name":"National Science Foundation","award":["GCR-2428487"],"award-info":[{"award-number":["GCR-2428487"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"\n Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have emerged as a tractable means to study such dynamics. Despite generating no entanglement in the computational basis, these circuits nevertheless capture many features expected from fully quantum evolutions. In this work, we demonstrate that the differences between automaton dynamics and fully quantum dynamics are revealed by the operator entanglement spectrum, much like the entanglement spectrum of a quantum state distinguishes between the dynamics of states under Clifford and Haar random circuits. While the operator entanglement spectrum under random unitary dynamics is governed by the eigenvalue statistics of random Gaussian matrices, we show evidence that under random automaton dynamics it is described by the statistics of Bernoulli random matrices, whose entries are random variables taking values\n \n 0<\/mml:mn>\n <\/mml:math>\n or\n \n 1<\/mml:mn>\n <\/mml:math>\n . We study the crossover between automaton and generic unitary operator dynamics as the automaton circuit is doped with gates that introduce superpositions, namely Hadamard or\n \n \n R<\/mml:mi>\n x<\/mml:mi>\n <\/mml:msub>\n =<\/mml:mo>\n \n e<\/mml:mi>\n \n &#x2212;<\/mml:mo>\n i<\/mml:mi>\n \n &#x03C0;<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:mfrac>\n X<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n gates. We find that a constant number of superposition-generating gates is sufficient to drive the operator dynamics to the random-circuit universality class, similar to earlier results on Clifford circuits doped with\n \n T<\/mml:mi>\n <\/mml:math>\n gates. This establishes the operator entanglement spectrum as a useful tool for probing the chaoticity and universality class of quantum dynamics.\n <\/jats:p>","DOI":"10.22331\/q-2026-03-05-2012","type":"journal-article","created":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T10:49:25Z","timestamp":1772707765000},"page":"2012","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum"],"prefix":"10.22331","volume":"10","author":[{"given":"Ben T.","family":"McDonough","sequence":"first","affiliation":[{"name":"Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA"},{"name":"Ames National Laboratory, Ames, IA 50011, USA"}]},{"given":"Claudio","family":"Chamon","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA"}]},{"given":"Justin H.","family":"Wilson","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA"},{"name":"Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA"}]},{"given":"Thomas","family":"Iadecola","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA"},{"name":"Ames National Laboratory, Ames, IA 50011, USA"},{"name":"Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA"},{"name":"Institute for Computational and Data Sciences, The Pennsylvania State University, University Park, PA 16802, USA"},{"name":"Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA"}]}],"member":"9598","published-online":{"date-parts":[[2026,3,5]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandra, Jeffrey Marshall, Charles Neill, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, et al. ``Information scrambling in quantum circuits''. 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