{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:10:50Z","timestamp":1792786250530,"version":"4.5.0"},"reference-count":94,"publisher":"American Physical Society (APS)","issue":"14","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12374477"],"award-info":[{"award-number":["12374477"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013105","name":"Shanghai Rising-Star Program","doi-asserted-by":"publisher","award":["24QA2700300"],"award-info":[{"award-number":["24QA2700300"]}],"id":[{"id":"10.13039\/501100013105","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018537","name":"National Science and Technology Major Project","doi-asserted-by":"publisher","award":["2024ZD0300101"],"award-info":[{"award-number":["2024ZD0300101"]}],"id":[{"id":"10.13039\/501100018537","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003347","name":"Fudan University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003347","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Quantum Science and Technology"},{"name":"Xuemin Institute of Advanced Studies","id":[{"id":"https:\/\/ror.org\/04t6wsp57","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Shanghai Qiguang Natural Science Development Foundation"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>Despite the rapid development of quantum science and technology, errors are inevitable and play a crucial role in quantum simulation and quantum computation. In quantum chaotic systems, coherent errors arising from imperfect Hamiltonian control and incoherent errors induced by coupling to the environment are both exponentially amplified during time evolution due to information scrambling. A fundamental question is how these two classes of errors imprint distinct signatures on the emergent irreversibility of many-body dynamics. In this Letter, we address this question by investigating multiround time-reversed dynamics in the presence of both coherent and incoherent errors. By applying scramblon theory, we obtain closed-form expressions for the Loschmidt echo over different rounds of time-reversed evolution. For incoherent errors, the error accumulates linearly with the number of rounds, whereas coherent errors exhibit a crossover from quadratic to linear accumulation. These predictions are explicitly verified using the solvable Sachdev-Ye-Kitaev model. Our results provide a theoretical foundation for characterizing and calibrating coherent and incoherent errors in reversed dynamics, with particular relevance to nuclear magnetic resonance systems.<\/jats:p>","DOI":"10.1103\/j72q-pf3h","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T12:49:38Z","timestamp":1788266978000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Distinguishing Coherent and Incoherent Errors in Multiround Time-Reversed Dynamics via Scramblons"],"prefix":"10.1103","volume":"137","author":[{"given":"Zeyu","family":"Liu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01vevwk45","id-type":"ROR","asserted-by":"publisher"}],"name":"Tsinghua University"},{"id":[{"id":"https:\/\/ror.org\/013q1eq08","id-type":"ROR","asserted-by":"publisher"}],"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7408-0918","authenticated-orcid":true,"given":"Pengfei","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/013q1eq08","id-type":"ROR","asserted-by":"publisher"}],"name":"Fudan University"},{"id":[{"id":"https:\/\/ror.org\/01jeedh73","id-type":"ROR","asserted-by":"publisher"}],"name":"Hefei National Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"j72q-pf3hCc1R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1261160","type":"journal-article"},{"key":"j72q-pf3hCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.031011","type":"journal-article"},{"key":"j72q-pf3hCc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.070501","type":"journal-article"},{"key":"j72q-pf3hCc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.090605","type":"journal-article"},{"key":"j72q-pf3hCc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.030601","type":"journal-article"},{"key":"j72q-pf3hCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.250601","type":"journal-article"},{"key":"j72q-pf3hCc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.104.012402","type":"journal-article"},{"key":"j72q-pf3hCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.105.052232","type":"journal-article"},{"key":"j72q-pf3hCc9R1","doi-asserted-by":"publisher","DOI":"10.1038\/nphys4119","type":"journal-article"},{"key":"j72q-pf3hCc10R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-0952-6","type":"journal-article"},{"key":"j72q-pf3hCc11R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-09436-y","type":"journal-article"},{"key":"j72q-pf3hCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.140601","type":"journal-article"},{"key":"j72q-pf3hCc13R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.abg5029","type":"journal-article"},{"key":"j72q-pf3hCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.4.043141","type":"journal-article"},{"key":"j72q-pf3hCc15R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-021-01430-w","type":"journal-article"},{"key":"j72q-pf3hCc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.160602","type":"journal-article"},{"key":"j72q-pf3hCc17R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-024-02664-0","type":"journal-article"},{"key":"j72q-pf3hCc19R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-022-01653-5","type":"journal-article"},{"key":"j72q-pf3hCc20R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.adg9500","type":"journal-article"},{"key":"j72q-pf3hCc21R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0537-1","type":"journal-article"},{"key":"j72q-pf3hCc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.126.070601","type":"journal-article"},{"key":"j72q-pf3hCc23R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-026-73520-3","type":"journal-article"},{"key":"j72q-pf3hCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/w1cp-l5vq","type":"journal-article"},{"key":"j72q-pf3hCc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.033197","type":"journal-article"},{"key":"j72q-pf3hCc26R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-09452-7","type":"journal-article"},{"key":"j72q-pf3hCc27R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP03(2014)067","type":"journal-article"},{"key":"j72q-pf3hCc28R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP03(2015)051","type":"journal-article"},{"key":"j72q-pf3hCc29R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP08(2016)106","type":"journal-article"},{"key":"j72q-pf3hCc30R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2015)132","type":"journal-article"},{"key":"j72q-pf3hCc31R1","unstructured":"A. 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systems without time-reversal symmetry, it is necessary to distinguish between scattering vertices located in the past and those in the future by introducing \u03d2VR\/A,m(t12).","type":"other"},{"key":"j72q-pf3hCc79R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/j72q-pf3h for (1)\u00a0a brief introduction to scramblon theory. (2)\u00a0Effective renormalization of scattering vertices. (3)\u00a0Discussion of a general number of rounds n. (4)\u00a0Details of SYK numerics. (5)\u00a0Finite temperature generation of the multiround Loschmidt echo. (6)\u00a0Exact calculations using scramblon theory verifying the behavior of Loschmidt echo with coherent error.","type":"other"},{"key":"j72q-pf3hCc80R1","unstructured":"Since \u03b4H is extensive, we expect \u03d2\u00af\u03b4H1\u221dN, and therefore \u03b3c\u223cO(1). In addition, the normalization of \u03b3c is chosen such that the single-round result satisfies F1(t)=fO(\u03b3ce\u03f0t), matching the incoherent case.","type":"other"},{"key":"j72q-pf3hCc81R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.37.43","type":"journal-article"},{"key":"j72q-pf3hCc82R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.432450","type":"journal-article"},{"key":"j72q-pf3hCc83R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.445185","type":"journal-article"},{"key":"j72q-pf3hCc84R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.449344","type":"journal-article"},{"key":"j72q-pf3hCc86R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP11(2019)038","type":"journal-article"},{"key":"j72q-pf3hCc87R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP12(2017)151","type":"journal-article"},{"key":"j72q-pf3hCc88R1","doi-asserted-by":"publisher","DOI":"10.1002\/prop.201700034","type":"journal-article"},{"key":"j72q-pf3hCc89R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.98.046016","type":"journal-article"},{"key":"j72q-pf3hCc90R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP10(2019)048","type":"journal-article"},{"key":"j72q-pf3hCc91R1","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.4.010320","type":"journal-article"},{"key":"j72q-pf3hCc92R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP07(2021)097","type":"journal-article"},{"key":"j72q-pf3hCc93R1","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.4.010321","type":"journal-article"},{"key":"j72q-pf3hCc94R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.12.031013","type":"journal-article"},{"key":"j72q-pf3hCc95R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-022-05424-3","type":"journal-article"},{"key":"j72q-pf3hCc96R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP07(2024)031","type":"journal-article"},{"key":"j72q-pf3hCc97R1","doi-asserted-by":"publisher","DOI":"10.1103\/j6j6-b3x8","type":"journal-article"},{"key":"j72q-pf3hCc98R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP11(2024)044","type":"journal-article"},{"key":"j72q-pf3hCc99R1","unstructured":"Z. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"140401"}}