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Quantum computing provides a promising route for overcoming these difficulties to find ground states, dynamics, and more. In this paper, we argue that recently developed hybrid quantum-classical algorithms based on real-time evolution are promising methods for solving a particularly important model in the search for spin liquids, the antiferromagnetic Heisenberg model on the two-dimensional kagome lattice. We show how to construct efficient quantum circuits to implement time evolution for the model and to evaluate key observables on the quantum computer, and we argue that the method has favorable scaling with increasing system size. We then restrict to a 12-spin star plaquette from the kagome lattice and a related 8-spin system, and we give an empirical demonstration on these small systems that the hybrid algorithms can efficiently find the ground state energy and the magnetization curve. For these demonstrations, we use four levels of approximation: exact state vectors, exact state vectors with statistical noise from sampling, noisy classical emulators, and (for the 8-spin system only) real quantum hardware, specifically the Quantinuum H1-1 processor; for the noisy simulations and hardware demonstration, we also employ error mitigation strategies based on the symmetries of the Hamiltonian. Our results strongly suggest that these hybrid algorithms present a promising direction for studying quantum spin liquids and more generally for resolving important unsolved problems in condensed matter theory and beyond.<\/jats:p>","DOI":"10.22331\/q-2025-04-09-1704","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T15:02:21Z","timestamp":1744210941000},"page":"1704","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1127-2111","authenticated-orcid":false,"given":"Aaron","family":"Szasz","sequence":"first","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1306-1860","authenticated-orcid":false,"given":"Ed","family":"Younis","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7114-8315","authenticated-orcid":false,"given":"Wibe Albert","family":"de Jong","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA"}]}],"member":"9598","published-online":{"date-parts":[[2025,4,9]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010).","DOI":"10.1038\/nature08917"},{"key":"1","doi-asserted-by":"publisher","unstructured":"L. Savary and L. Balents, Quantum spin liquids: a review, Reports on Progress in Physics 80, 016502 (2016).","DOI":"10.1088\/0034-4885\/80\/1\/016502"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).","DOI":"10.1103\/RevModPhys.89.025003"},{"key":"3","doi-asserted-by":"publisher","unstructured":"P. Anderson, Resonating valence bonds: A new kind of insulator?, Materials Research Bulletin 8, 153 (1973).","DOI":"10.1016\/0025-5408(73)90167-0"},{"key":"4","doi-asserted-by":"publisher","unstructured":"D. A. Huse and V. Elser, Simple Variational Wave Functions for Two-Dimensional Heisenberg Spin-$\\frac{1}{2}$ Antiferromagnets, Phys. Rev. Lett. 60, 2531 (1988).","DOI":"10.1103\/PhysRevLett.60.2531"},{"key":"5","doi-asserted-by":"publisher","unstructured":"S. R. White and A. L. Chernyshev, Ne\u00e9l Order in Square and Triangular Lattice Heisenberg Models, Phys. Rev. Lett. 99, 127004 (2007).","DOI":"10.1103\/PhysRevLett.99.127004"},{"key":"6","doi-asserted-by":"publisher","unstructured":"R. Kaneko, S. Morita, and M. Imada, Gapless Spin-Liquid Phase in an Extended Spin 1\/2 Triangular Heisenberg Model, Journal of the Physical Society of Japan 83, 093707 (2014).","DOI":"10.7566\/JPSJ.83.093707"},{"key":"7","doi-asserted-by":"publisher","unstructured":"W.-J. Hu, S.-S. Gong, W. Zhu, and D. N. Sheng, Competing spin-liquid states in the spin-$\\frac{1}{2}$ Heisenberg model on the triangular lattice, Phys. Rev. B 92, 140403 (2015).","DOI":"10.1103\/PhysRevB.92.140403"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Z. Zhu and S. R. White, Spin liquid phase of the $S=\\frac{1}{2}\\phantom{\\rule{4.pt}{0ex}}{J}_{1}{-}{J}_{2}$ Heisenberg model on the triangular lattice, Phys. Rev. B 92, 041105 (2015).","DOI":"10.1103\/PhysRevB.92.041105"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Y. Iqbal, W.-J. Hu, R. Thomale, D. Poilblanc, and F. Becca, Spin liquid nature in the Heisenberg ${J}_{1}{-}{J}_{2}$ triangular antiferromagnet, Phys. Rev. B 93, 144411 (2016).","DOI":"10.1103\/PhysRevB.93.144411"},{"key":"10","doi-asserted-by":"publisher","unstructured":"S. Hu, W. Zhu, S. Eggert, and Y.-C. He, Dirac Spin Liquid on the Spin-$1\/2$ Triangular Heisenberg Antiferromagnet, Phys. Rev. Lett. 123, 207203 (2019).","DOI":"10.1103\/PhysRevLett.123.207203"},{"key":"11","doi-asserted-by":"publisher","unstructured":"O. I. Motrunich, Variational study of triangular lattice spin-$1\/2$ model with ring exchanges and spin liquid state in ${\\kappa}\\text{{-}}{(\\mathrm{ET})}_{2}{\\mathrm{Cu}}_{2}{(\\mathrm{CN})}_{3}$, Phys. Rev. B 72, 045105 (2005).","DOI":"10.1103\/PhysRevB.72.045105"},{"key":"12","doi-asserted-by":"publisher","unstructured":"H.-Y. Yang, A. M. L\u00e4uchli, F. Mila, and K. P. Schmidt, Effective Spin Model for the Spin-Liquid Phase of the Hubbard Model on the Triangular Lattice, Phys. Rev. Lett. 105, 267204 (2010).","DOI":"10.1103\/PhysRevLett.105.267204"},{"key":"13","doi-asserted-by":"publisher","unstructured":"R. V. Mishmash, J. R. Garrison, S. Bieri, and C. Xu, Theory of a Competitive Spin Liquid State for Weak Mott Insulators on the Triangular Lattice, Phys. Rev. Lett. 111, 157203 (2013).","DOI":"10.1103\/PhysRevLett.111.157203"},{"key":"14","doi-asserted-by":"publisher","unstructured":"T. Shirakawa, T. Tohyama, J. Kokalj, S. Sota, and S. Yunoki, Ground-state phase diagram of the triangular lattice Hubbard model by the density-matrix renormalization group method, Phys. Rev. B 96, 205130 (2017).","DOI":"10.1103\/PhysRevB.96.205130"},{"key":"15","doi-asserted-by":"publisher","unstructured":"A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study, Phys. Rev. X 10, 021042 (2020).","DOI":"10.1103\/PhysRevX.10.021042"},{"key":"16","doi-asserted-by":"publisher","unstructured":"L. F. Tocchio, A. Montorsi, and F. Becca, Magnetic and spin-liquid phases in the frustrated $t{-}{t}^{{&apos;}}$ Hubbard model on the triangular lattice, Phys. Rev. B 102, 115150 (2020).","DOI":"10.1103\/PhysRevB.102.115150"},{"key":"17","doi-asserted-by":"publisher","unstructured":"A. Szasz and J. Motruk, Phase diagram of the anisotropic triangular lattice Hubbard model, Phys. Rev. B 103, 235132 (2021).","DOI":"10.1103\/PhysRevB.103.235132"},{"key":"18","doi-asserted-by":"publisher","unstructured":"L. F. Tocchio, A. Montorsi, and F. 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Wang, Prepare Ground States of Highly Frustrated Magnetic Clusters on Quantum Computers, in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), Vol. 02 (2023) pp. 397\u2013398.","DOI":"10.1109\/QCE57702.2023.10300"},{"key":"56","doi-asserted-by":"publisher","unstructured":"C. L. Cortes and S. K. Gray, Quantum Krylov subspace algorithms for ground- and excited-state energy estimation, Phys. Rev. A 105, 022417 (2022).","DOI":"10.1103\/PhysRevA.105.022417"},{"key":"57","doi-asserted-by":"publisher","unstructured":"M. B. Hastings, An area law for one-dimensional quantum systems, Journal of Statistical Mechanics: Theory and Experiment 2007, P08024 (2007).","DOI":"10.1088\/1742-5468\/2007\/08\/P08024"},{"key":"58","doi-asserted-by":"publisher","unstructured":"I. Arad, A. Kitaev, Z. Landau, and U. Vazirani, An area law and sub-exponential algorithm for 1D systems, arXiv (2013), arXiv:1301.1162 [quant-ph].","DOI":"10.48550\/arXiv.1301.1162"},{"key":"59","doi-asserted-by":"publisher","unstructured":"R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Quantum algorithms revisited, Proc. Roy. Soc. Lond. A 454, 339 (1998).","DOI":"10.1098\/rspa.1998.0164"},{"key":"60","doi-asserted-by":"publisher","unstructured":"E. K\u00f6kc\u00fc, D. Camps, L. B. Oftelie, W. A. de Jong, R. V. Beeumen, and A. F. Kemper, Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution, arXiv (2023), arXiv:2303.09538 [quant-ph].","DOI":"10.48550\/arXiv.2303.09538"},{"key":"61","doi-asserted-by":"publisher","unstructured":"V. Havl\u00ed\u010dek, A. D. C\u00f3rcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. 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