{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T04:55:55Z","timestamp":1776920155993,"version":"3.51.2"},"reference-count":53,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"},{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Financiamiento Basal"},{"DOI":"10.13039\/501100003086","name":"Eusko Jaurlaritza","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"name":"MCIU\/AEI\/FEDER, UE"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"Abstract<\/jats:title>\n The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrix \n \n\n<\/jats:tex-math>\n \n \n \n \n \n U<\/mml:mi>\n <\/mml:mrow>\n \n \u02c6<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mover>\n <\/mml:mrow>\n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n =<\/mml:mo>\n \n \n e<\/mml:mi>\n <\/mml:mrow>\n \n \u2212<\/mml:mo>\n i<\/mml:mi>\n \u03c4<\/mml:mi>\n \n \n \n \n \ue23b<\/mml:mi>\n <\/mml:mrow>\n \n \u02c6<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mover>\n <\/mml:mrow>\n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n \n <\/jats:inline-formula> where \n \n\n<\/jats:tex-math>\n \n \n \n \n \n \ue23b<\/mml:mi>\n <\/mml:mrow>\n \n \u02c6<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mover>\n <\/mml:mrow>\n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n \n <\/jats:inline-formula> is a Hermitian operator, and \u03c4<\/jats:italic> is a real parameter. The agent is a quantum state which adapts to some eigenvector of \n \n\n<\/jats:tex-math>\n \n \n \n \n \n \ue23b<\/mml:mi>\n <\/mml:mrow>\n \n \u02c6<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mover>\n <\/mml:mrow>\n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n \n <\/jats:inline-formula> by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90% in less than 10 iterations, and surpass 98% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89% in 8000 iterations for a random operator, and fidelities of 99% for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention.<\/jats:p>","DOI":"10.1088\/2632-2153\/ab43b4","type":"journal-article","created":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T17:52:17Z","timestamp":1580838737000},"page":"015002","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["Reinforcement learning for semi-autonomous approximate quantum eigensolver"],"prefix":"10.1088","volume":"1","author":[{"given":"F","family":"Albarr\u00e1n-Arriagada","sequence":"first","affiliation":[]},{"given":"J C","family":"Retamal","sequence":"additional","affiliation":[]},{"given":"E","family":"Solano","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9504-8685","authenticated-orcid":false,"given":"L","family":"Lamata","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,2,4]]},"reference":[{"key":"mlstab43b4bib1","author":"Adcock","year":"2015"},{"key":"mlstab43b4bib2","doi-asserted-by":"publisher","DOI":"10.1038\/nature23474","article-title":"Quantum machine learning","volume":"549","author":"Biamonte","year":"2017","journal-title":"Nature"},{"key":"mlstab43b4bib3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.130501","article-title":"Quantum-enhanced machine learning","volume":"117","author":"Dunjko","year":"2016","journal-title":"Phys. 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