{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T14:14:44Z","timestamp":1789049684330,"version":"build-2803163510"},"reference-count":43,"publisher":"American Physical Society (APS)","issue":"3","license":[{"start":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T00:00:00Z","timestamp":1788998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Autretech Group"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,7,28]]},"abstract":"<jats:p>The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state, projective operators, unitary learning, and others), semidefinite programming () can be applied to solve the fidelity optimization problem with respect to the Choi matrix. A remarkable feature of  is that the optimization is convex, which allows the problem to be efficiently solved by a variety of numerical algorithms. We have tested several commercially available  solvers, all of which allowed for the reconstruction of quantum channels of different forms. A notable feature is that the Kraus rank of the obtained quantum channel typically comprises less than a few percent of its maximal possible value. This suggests that a relatively small Kraus rank quantum channel is typically sufficient to describe experimentally observed classical data. The theory was also applied to the problem of reconstructing projective operators from data. Finally, we discuss a classical computational model based on quantum channel transformation, performed and calculated on a classical computer, possibly hardware-optimized.<\/jats:p>","DOI":"10.1103\/kdl5-smrh","type":"journal-article","created":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T13:36:06Z","timestamp":1785245766000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Semidefinite programming for quantum channel learning"],"prefix":"10.1103","volume":"114","author":[{"given":"Mikhail Gennadievich","family":"Belov","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/010pmpe69","id-type":"ROR","asserted-by":"publisher"}],"name":"Lomonosov Moscow State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Victor Victorovich","family":"Dubov","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02x91aj62","id-type":"ROR","asserted-by":"publisher"}],"name":"Peter the Great St. Petersburg Polytechnic University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3584-4583","authenticated-orcid":true,"given":"Vadim Konstantinovich","family":"Ivanov","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02x91aj62","id-type":"ROR","asserted-by":"publisher"}],"name":"Peter the Great St. Petersburg Polytechnic University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6296-5988","authenticated-orcid":true,"given":"Alexander Yurievich","family":"Maslov","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05dkdaa55","id-type":"ROR","asserted-by":"publisher"}],"name":"Ioffe Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0087-5838","authenticated-orcid":true,"given":"Olga Vladimirovna","family":"Proshina","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05dkdaa55","id-type":"ROR","asserted-by":"publisher"}],"name":"Ioffe Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0429-3456","authenticated-orcid":true,"given":"Vladislav Gennadievich","family":"Malyshkin","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05dkdaa55","id-type":"ROR","asserted-by":"publisher"}],"name":"Ioffe Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,9,10]]},"reference":[{"key":"kdl5-smrhCc1R1","first-page":"21","type":"journal-article","volume":"8","author":"V. 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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":"035302"}}