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In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.<\/jats:p>","DOI":"10.22331\/q-2023-12-20-1213","type":"journal-article","created":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T15:57:47Z","timestamp":1703087867000},"page":"1213","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":45,"title":["General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7288-2810","authenticated-orcid":false,"given":"Zohreh","family":"Davoudi","sequence":"first","affiliation":[{"name":"Department of Physics, University of Maryland, College Park, MD 20742, USA"},{"name":"Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA"},{"name":"Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, College Park, MD 20742, USA"},{"name":"The NSF Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander F.","family":"Shaw","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Maryland, College Park, MD 20742, USA"},{"name":"Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, College Park, MD 20742, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4968-7988","authenticated-orcid":false,"given":"Jesse R.","family":"Stryker","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Maryland, College Park, MD 20742, USA"},{"name":"Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA"},{"name":"Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,12,20]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Richard P. 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