{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T07:30:46Z","timestamp":1768289446357,"version":"3.49.0"},"reference-count":41,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T00:00:00Z","timestamp":1719446400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"German Federal Ministry of Education and Research","award":["13N15890"],"award-info":[{"award-number":["13N15890"]}]},{"name":"German Federal Ministry of Education and Research","award":["13N16066"],"award-info":[{"award-number":["13N16066"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["EXC-2111 \u2013 390814868"],"award-info":[{"award-number":["EXC-2111 \u2013 390814868"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"EU- QUANTERA","award":["BA 6059\/1-1"],"award-info":[{"award-number":["BA 6059\/1-1"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width &#x03B4;<\/mml:mi><\/mml:math>. Given a local Hamiltonian on N<\/mml:mi><\/mml:math> qubits, we construct a parent Hamiltonian whose ground state corresponds to the filtered product state with variable energy variance proportional to &#x03B4;<\/mml:mi>N<\/mml:mi><\/mml:msqrt><\/mml:math>. We prove that the parent Hamiltonian is gapped and its ground state can be efficiently implemented in p<\/mml:mi>o<\/mml:mi>l<\/mml:mi>y<\/mml:mi><\/mml:mrow>(<\/mml:mo>N<\/mml:mi>,<\/mml:mo>1<\/mml:mn>\/<\/mml:mo><\/mml:mrow>&#x03B4;<\/mml:mi>)<\/mml:mo><\/mml:math> time via adiabatic evolution. We numerically benchmark the algorithm for a particular non-integrable model and find that the adiabatic evolution time to prepare the filtered state with a width &#x03B4;<\/mml:mi><\/mml:math> is independent of the system size N<\/mml:mi><\/mml:math>. Furthermore, the adiabatic evolution can be implemented with circuit depth O<\/mml:mi><\/mml:mrow>(<\/mml:mo>N<\/mml:mi>2<\/mml:mn><\/mml:msup>&#x03B4;<\/mml:mi>&#x2212;<\/mml:mo>4<\/mml:mn><\/mml:mrow><\/mml:msup>)<\/mml:mo><\/mml:math>. Our algorithm provides a way to study the finite energy regime of many body systems in quantum simulators by directly preparing a finite energy state, providing access to an approximation of the microcanonical properties at an arbitrary energy.<\/jats:p>","DOI":"10.22331\/q-2024-06-27-1389","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T12:20:58Z","timestamp":1719490858000},"page":"1389","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Efficient Quantum Algorithm for Filtering Product States"],"prefix":"10.22331","volume":"8","author":[{"given":"Reinis","family":"Irmejs","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstra\u00dfe 4, D-80799 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mari Carmen","family":"Ba\u00f1uls","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstra\u00dfe 4, D-80799 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. Ignacio","family":"Cirac","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstra\u00dfe 4, D-80799 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2024,6,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"David Deutsch. ``Quantum theory, the church\u2013turing principle and the universal quantum computer''. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 400, 97\u2013117 (1985).","DOI":"10.1098\/rspa.1985.0070"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Seth Lloyd. ``Universal quantum simulators''. 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