{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T04:32:35Z","timestamp":1774067555083,"version":"3.50.1"},"reference-count":35,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T00:00:00Z","timestamp":1710288000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained by a quantum computer. The recently proposed Variational Quantum Phase Estimation (VQPE) algorithm uses a basis of real time-evolved states, for which the energy eigenvalues can be obtained directly from the unitary matrix U<\/mml:mi>=<\/mml:mo>e<\/mml:mi>&#x2212;<\/mml:mo>i<\/mml:mi>H<\/mml:mi>&#x0394;<\/mml:mi><\/mml:mrow>t<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:math>, which can be computed with cost linear in the number of states used. In this paper, we report a circuit-based implementation of VQPE for arbitrary molecular systems and assess its performance and costs for the H<\/mml:mi>2<\/mml:mn><\/mml:msub><\/mml:math>, H<\/mml:mi>3<\/mml:mn>+<\/mml:mo><\/mml:msubsup><\/mml:math> and H<\/mml:mi>6<\/mml:mn><\/mml:msub><\/mml:math> molecules. We also propose using Variational Fast Forwarding (VFF) to decrease to quantum depth of time-evolution circuits for use in VQPE. We show that the approximation provides a good basis for Hamiltonian diagonalisation even when its fidelity to the true time evolved states is low. In the high fidelity case, we show that the approximate unitary U can be diagonalised instead, preserving the linear cost of exact VQPE.<\/jats:p>","DOI":"10.22331\/q-2024-03-13-1278","type":"journal-article","created":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T11:39:12Z","timestamp":1710329952000},"page":"1278","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Variational Phase Estimation with Variational Fast Forwarding"],"prefix":"10.22331","volume":"8","author":[{"given":"Maria-Andreea","family":"Filip","sequence":"first","affiliation":[{"name":"Quantinuum, 13-15 Hills Road, CB2 1NL, Cambridge, United Kingdom"},{"name":"Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom"}]},{"given":"David Mu\u00f1oz","family":"Ramo","sequence":"additional","affiliation":[{"name":"Quantinuum, 13-15 Hills Road, CB2 1NL, Cambridge, United Kingdom"}]},{"given":"Nathan","family":"Fitzpatrick","sequence":"additional","affiliation":[{"name":"Quantinuum, 13-15 Hills Road, CB2 1NL, Cambridge, United Kingdom"}]}],"member":"9598","published-online":{"date-parts":[[2024,3,13]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"John Preskill. ``Quantum Computing in the NISQ era and beyond''. 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