{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T12:24:00Z","timestamp":1751718240115},"reference-count":48,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T00:00:00Z","timestamp":1638403200000},"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":"<jats:p>Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such consideration is size-extensivity, meaning that the ground state quantum correlations are to be compactly represented in the ansatz. On digital quantum computers, however, the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods. These introduce additional costs and errors to the approximation. In this work, we present a diagrammatic scheme for the digital VQE ansatzes, which is size-extensive but does not rely on Trotterization. We start by designing a family of digital ansatzes that explore the entire Hilbert space with the minimum number of free parameters. We then demonstrate how one may compress an arbitrary digital ansatz, by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism that ensures the size-extensivity of generated hierarchies. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.<\/jats:p>","DOI":"10.22331\/q-2021-12-02-596","type":"journal-article","created":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T16:24:12Z","timestamp":1638462252000},"page":"596","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["A diagrammatic approach to variational quantum ansatz construction"],"prefix":"10.22331","volume":"5","author":[{"given":"Y.","family":"Herasymenko","sequence":"first","affiliation":[{"name":"Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands"}]},{"given":"T.E.","family":"O'Brien","sequence":"additional","affiliation":[{"name":"Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands"}]}],"member":"9598","published-online":{"date-parts":[[2021,12,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018).","DOI":"10.22331\/q-2018-08-06-79"},{"key":"1","doi-asserted-by":"publisher","unstructured":"D. Litinski, Magic State Distillation: Not as Costly as You Think, Quantum 3, 205 (2019).","DOI":"10.22331\/q-2019-12-02-205"},{"key":"2","doi-asserted-by":"publisher","unstructured":"A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J.Love, A. Aspuru-Guzik, and J. L. O\u2019Brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Comm. 5, 4213 (2014).","DOI":"10.1038\/ncomms5213"},{"key":"3","doi-asserted-by":"publisher","unstructured":"J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New J. 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