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We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen low-depth fermion-to-qubit mappings and allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>70<\/mml:mn><mml:mi mathvariant=\"normal\">&amp;#x0025;<\/mml:mi><\/mml:math> improvement upon previous state-of-the-art. Our compression technique also results in significant reduction of two-qubit gates. We find the lowest gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.<\/jats:p>","DOI":"10.22331\/q-2024-04-30-1327","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T15:56:16Z","timestamp":1714492576000},"page":"1327","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Low-depth simulations of fermionic systems on square-grid quantum hardware"],"prefix":"10.22331","volume":"8","author":[{"given":"Manuel G.","family":"Algaba","sequence":"first","affiliation":[{"name":"IQM, Nymphenburgerstr. 86, 80636 Munich, Germany"}]},{"given":"P. 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