{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T02:37:10Z","timestamp":1770345430177,"version":"3.49.0"},"reference-count":35,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:00:00Z","timestamp":1725494400000},"content-version":"vor","delay-in-days":4,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:00:00Z","timestamp":1725494400000},"content-version":"tdm","delay-in-days":4,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We propose a support vector machine (SVM) based approach for generating an entanglement witness that requires exponentially less training data than previously proposed methods. SVMs generate hyperplanes represented by a weighted sum of expectation values of local observables whose coefficients are optimized to sum to a positive number for all separable states and a negative number for as many entangled states as possible near a specific target state. Previous SVM-based approaches for entanglement witness generation used large amounts of randomly generated separable states to perform training, a task with considerable computational overhead. Here, we propose a method for orienting the witness hyperplane using only the significantly smaller set of states consisting of the eigenstates of the generalized Pauli matrices and a set of entangled states near the target entangled states. With the orientation of the witness hyperplane set by the SVM, we tune the plane\u2019s placement using a differential program that ensures perfect classification accuracy on a limited test set as well as maximal noise tolerance. For <jats:italic>N<\/jats:italic> qubits, the SVM portion of this approach requires only <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mi>O<\/mml:mi>\n                           <mml:mo stretchy=\"false\">(<\/mml:mo>\n                           <mml:msup>\n                              <mml:mn>6<\/mml:mn>\n                              <mml:mi>N<\/mml:mi>\n                           <\/mml:msup>\n                           <mml:mo stretchy=\"false\">)<\/mml:mo>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula> training states, whereas an existing method needs <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mi>O<\/mml:mi>\n                           <mml:mo stretchy=\"false\">(<\/mml:mo>\n                           <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mrow>\n                                 <mml:msup>\n                                    <mml:mn>4<\/mml:mn>\n                                    <mml:mi>N<\/mml:mi>\n                                 <\/mml:msup>\n                              <\/mml:mrow>\n                           <\/mml:msup>\n                           <mml:mo stretchy=\"false\">)<\/mml:mo>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula>. We use this method to construct witnesses of 4 and 5 qubit GHZ states with coefficients agreeing with stabilizer formalism witnesses to within 3.7 percent and 1 percent, respectively. We also use the same training states to generate novel 4 and 5 qubit W state witnesses. Finally, we computationally verify these witnesses on small test sets and propose methods for further verification.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad7457","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T23:03:55Z","timestamp":1724799835000},"page":"035068","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["An exponential reduction in training data sizes for machine learning derived entanglement witnesses"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6042-0035","authenticated-orcid":true,"given":"Aiden R","family":"Rosebush","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander C B","family":"Greenwood","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brian T","family":"Kirby","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Qian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,9,5]]},"reference":[{"key":"mlstad7457bib1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.060503","article-title":"Large-alphabet quantum key distribution using energy-time entangled bipartite states","volume":"98","author":"Ali-Khan","year":"2007","journal-title":"Phys. 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Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2024-02-26","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-08-27","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-09-05","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}