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Department of Energy","doi-asserted-by":"crossref","award":["ERKJ347"],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number ofT<\/mml:mi><\/mml:math>gates that grows asO<\/mml:mi><\/mml:mrow>(<\/mml:mo>N<\/mml:mi>5<\/mml:mn><\/mml:msup>)<\/mml:mo><\/mml:mrow><\/mml:math>per time step to calculate the impurity Green's function in the time domain, whereN<\/mml:mi><\/mml:math>is the total number of energy levels in the AIM. Since the number ofT<\/mml:mi><\/mml:math>gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requiresO<\/mml:mi><\/mml:mrow>(<\/mml:mo>N<\/mml:mi>6<\/mml:mn><\/mml:msup>)<\/mml:mo><\/mml:mrow><\/mml:math>computational resources per time step.<\/jats:p>","DOI":"10.22331\/q-2022-03-30-675","type":"journal-article","created":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T13:53:31Z","timestamp":1648648411000},"page":"675","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Hybrid quantum-classical approach for coupled-cluster Green&apos;s function theory"],"prefix":"10.22331","volume":"6","author":[{"given":"Trevor","family":"Keen","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States of America"}]},{"given":"Bo","family":"Peng","sequence":"additional","affiliation":[{"name":"Physical Sciences and Computational Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States of America"}]},{"given":"Karol","family":"Kowalski","sequence":"additional","affiliation":[{"name":"Physical Sciences and Computational Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States of America"}]},{"given":"Pavel","family":"Lougovski","sequence":"additional","affiliation":[{"name":"Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America"}]},{"given":"Steven","family":"Johnston","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States of America"},{"name":"Institute for Advanced Materials and Manufacturing, University of Tennessee, Knoxville, Tennessee 37996, United States of America"}]}],"member":"9598","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Gadi Aleksandrowicz, Thomas Alexander, Panagiotis Barkoutsos, Luciano Bello, Yael Ben-Haim, David Bucher, Francisco Jose Cabrera-Hern\u00e1ndez, Jorge Carballo-Franquis, Adrian Chen, Chun-Fu Chen, Jerry M. 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