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We describe an operational procedure for constructing the approximate description of the state that requires, besides the quantum state preparation, only single-qubit rotations followed by single-qubit measurements. We show that following this procedure, the cardinality of the resulting description of the state grows as <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>3<\/mml:mn><mml:mi>M<\/mml:mi><mml:mi>N<\/mml:mi><\/mml:math>. We test the proposed method on Rigetti's quantum processor unit with 12, 16 and 25 qubits for random states and random observables, and find an excellent agreement with the theory, despite experimental errors.<\/jats:p>","DOI":"10.22331\/q-2021-03-16-413","type":"journal-article","created":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T14:47:45Z","timestamp":1615906065000},"page":"413","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":25,"title":["Estimating expectation values using approximate quantum states"],"prefix":"10.22331","volume":"5","author":[{"given":"Marco","family":"Paini","sequence":"first","affiliation":[{"name":"Rigetti Computing, 138 Holborn, London, EC1N 2SW, UK."}]},{"given":"Amir","family":"Kalev","sequence":"additional","affiliation":[{"name":"Information Sciences Institute, University of Southern California, Arlington, VA 22203, USA."}]},{"given":"Dan","family":"Padilha","sequence":"additional","affiliation":[{"name":"Rigetti Computing, 138 Holborn, London, EC1N 2SW, UK."}]},{"given":"Brendan","family":"Ruck","sequence":"additional","affiliation":[{"name":"Rigetti Computing, 2919 Seventh St, Berkeley, CA 94710, USA."}]}],"member":"9598","published-online":{"date-parts":[[2021,3,16]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"G. 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