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In these applications, computing a compressed representation of the MPO-MPS product is a fundamental computational primitive. For this operation, this paper introduces a new single-pass, randomized algorithm, called successive randomized compression (SRC), that improves on existing approaches in speed or in accuracy. The performance of the new algorithm is evaluated on synthetic problems and unitary time evolution problems for quantum spin systems.<\/jats:p>","DOI":"10.22331\/q-2026-03-10-2022","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T15:20:44Z","timestamp":1773156044000},"page":"2022","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Successive randomized compression: A randomized algorithm for the compressed MPO-MPS product"],"prefix":"10.22331","volume":"10","author":[{"given":"Chris","family":"Cama\u00f1o","sequence":"first","affiliation":[{"name":"Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, 91125, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0712-8296","authenticated-orcid":false,"given":"Ethan N.","family":"Epperly","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, 91125, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1024-1791","authenticated-orcid":false,"given":"Joel A.","family":"Tropp","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, 91125, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,3,10]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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