{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:01:50Z","timestamp":1760151710808,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T00:00:00Z","timestamp":1649808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000015","name":"United States Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0019469"],"award-info":[{"award-number":["DE-SC0019469"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMR-1752713"],"award-info":[{"award-number":["DMR-1752713"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006192","name":"Office of Advanced Scientific Computing Research","doi-asserted-by":"publisher","award":["ERKJ347"],"award-info":[{"award-number":["ERKJ347"]}],"id":[{"id":"10.13039\/100006192","id-type":"DOI","asserted-by":"publisher"}]},{"name":"McDevitt bequest at Georgetown","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on classical computers, but are challenging on quantum computers because of the accuracy needed and the near degeneracy of the competing states close to the level crossings. On the other hand, classical computers are limited to small system sizes, which quantum computers may help overcome. In this work, we use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. This methodology is illustrated by examining the ground states of the XY model with a magnetic field in the z-direction in one dimension. We are able to calculate an accurate phase diagram on both two- and three-site systems using IBM quantum machines.<\/jats:p>","DOI":"10.3390\/sym14040809","type":"journal-article","created":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T23:07:16Z","timestamp":1649891236000},"page":"809","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Determining Ground-State Phase Diagrams on Quantum Computers via a Generalized Application of Adiabatic State Preparation"],"prefix":"10.3390","volume":"14","author":[{"given":"Akhil","family":"Francis","sequence":"first","affiliation":[{"name":"Department of Physics, North Carolina State University, Raleigh, NC 27695, USA"}]},{"given":"Ephrata","family":"Zelleke","sequence":"additional","affiliation":[{"name":"Department of Physics, Goucher College, Baltimore, MD 21204, USA"}]},{"given":"Ziyue","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Physics, Georgetown University, Washington, DC 20057, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5426-5181","authenticated-orcid":false,"given":"Alexander F.","family":"Kemper","sequence":"additional","affiliation":[{"name":"Department of Physics, North Carolina State University, Raleigh, NC 27695, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6232-9165","authenticated-orcid":false,"given":"James K.","family":"Freericks","sequence":"additional","affiliation":[{"name":"Department of Physics, Georgetown University, Washington, DC 20057, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1126\/science.273.5278.1073","article-title":"Universal quantum simulators","volume":"273","author":"Lloyd","year":"1996","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2586","DOI":"10.1103\/PhysRevLett.79.2586","article-title":"Simulation of many-body Fermi systems on a universal quantum computer","volume":"79","author":"Abrams","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1103\/RevModPhys.86.153","article-title":"Quantum simulation","volume":"86","author":"Georgescu","year":"2014","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/npjqi.2015.23","article-title":"Quantum algorithms: An overview","volume":"2","author":"Montanaro","year":"2016","journal-title":"NPJ Quantum Inf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9456","DOI":"10.1073\/pnas.1801723115","article-title":"Toward the first quantum simulation with quantum speedup","volume":"115","author":"Childs","year":"2018","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qin, M., Sch\u00e4fer, T., Andergassen, S., Corboz, P., and Gull, E. (2021). The Hubbard model: A computational perspective. arXiv.","DOI":"10.1146\/annurev-conmatphys-090921-033948"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2069","DOI":"10.1088\/0034-4885\/66\/12\/R01","article-title":"Quantum phase transitions","volume":"66","author":"Vojta","year":"2003","journal-title":"Rep. Prog. Phys."},{"key":"ref_8","first-page":"238","article-title":"Electron correlations in narrow energy bands","volume":"276","author":"Hubbard","year":"1963","journal-title":"Proc. R. Soc. Lond. Ser. Math. Phys. Sci."},{"key":"ref_9","unstructured":"Farhi, E., Goldstone, J., and Gutmann, S. (2014). A quantum approximate optimization algorithm. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"063002","DOI":"10.1103\/PhysRevLett.104.063002","article-title":"Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity","volume":"104","author":"Chen","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"045001","DOI":"10.1103\/RevModPhys.91.045001","article-title":"Shortcuts to adiabaticity: Concepts, methods, and applications","volume":"91","author":"Ruschhaupt","year":"2019","journal-title":"Rev. Mod. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1103\/PhysRevLett.49.249","article-title":"One-Dimensional Ising Model and the Complete Devil\u2019s Staircase","volume":"49","author":"Bak","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"100506","DOI":"10.1103\/PhysRevLett.111.100506","article-title":"Quantum catalysis of magnetic phase transitions in a quantum simulator","volume":"111","author":"Richerme","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1007\/BF01331938","article-title":"Pauli\u2019s equivalence prohibition","volume":"47","author":"Jordan","year":"1928","journal-title":"Z. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0003-4916(61)90115-4","article-title":"Two soluble models of an antiferromagnetic chain","volume":"16","author":"Lieb","year":"1961","journal-title":"Ann. Phys."},{"key":"ref_16","unstructured":"Mbeng, G.B., Russomanno, A., and Santoro, G.E. (2020). The quantum Ising chain for beginners. arXiv."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"042308","DOI":"10.1103\/PhysRevA.65.042308","article-title":"Quantum search by local adiabatic evolution","volume":"65","author":"Roland","year":"2002","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"012334","DOI":"10.1103\/PhysRevA.88.012334","article-title":"Experimental performance of a quantum simulator: Optimizing adiabatic evolution and identifying many-body ground states","volume":"88","author":"Richerme","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_19","unstructured":"Andersson, S., Asfaw, A., Corcoles, A., Bello, L., Ben-Haim, Y., Bozzo-Rey, M., Bravyi, S., Bronn, N., Capelluto, L., and Vazquez, A.C. (2022, January 24). Learn Quantum Computation Using Qiskit. Available online: http:\/\/community.qiskit.org\/textbook."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"010301","DOI":"10.1103\/PhysRevA.69.010301","article-title":"A universal quantum circuit for two-qubit transformations with three CNOT gates","volume":"69","author":"Vidal","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1038\/s41567-019-0437-4","article-title":"Quantum hardware simulating four-dimensional inelastic neutron scattering","volume":"15","author":"Chiesa","year":"2019","journal-title":"Nat. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"014411","DOI":"10.1103\/PhysRevB.101.014411","article-title":"Quantum computation of magnon spectra","volume":"101","author":"Francis","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_23","unstructured":"Rost, B., Del Re, L., Earnest, N., Kemper, A.F., Jones, B., and Freericks, J.K. (2021). Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers. arXiv."},{"key":"ref_24","unstructured":"Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Bengtsson, A., Boixo, S., Broughton, M., and Buckley, B.B. (2020). Observation of separated dynamics of charge and spin in the fermi-hubbard model. arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"062309","DOI":"10.1103\/PhysRevA.63.062309","article-title":"Optimal Creation of Entanglement Using a Two\u2013Qubit Gate","volume":"63","author":"Kraus","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"K\u00f6kc\u00fc, E., Steckmann, T., Freericks, J., Dumitrescu, E.F., and Kemper, A.F. (2021). Fixed depth hamiltonian simulation via cartan decomposition. arXiv.","DOI":"10.1103\/PhysRevLett.129.070501"},{"key":"ref_27","first-page":"011020","article-title":"Theory of trotter error with commutator scaling","volume":"11","author":"Childs","year":"2021","journal-title":"Phys. Rev. X"},{"key":"ref_28","unstructured":"Aleksandrowicz, G., Alexander, T., Barkoutsos, P., Bello, L., Ben-Haim, Y., Bucher, D., Cabrera-Hern\u00e1ndez, F.J., Carballo-Franquis, J., Chen, A., and Chen, C.F. (2022, February 21). Qiskit: An Open-Source Framework for Quantum Computing. Available online: https:\/\/zenodo.org\/record\/2562111#.YlYzptNByUl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/809\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:53:07Z","timestamp":1760136787000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/809"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,13]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["sym14040809"],"URL":"https:\/\/doi.org\/10.3390\/sym14040809","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,4,13]]}}}