Low-depth simulations of fermionic systems on realistic quantum hardware

We introduce a general strategy for mapping fermionic systems to quantum hardware with realistic qubit connectivity which results in low-depth quantum circuits as counted by the number of native two-qubit gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen fermion-to-qubit mappings that allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimise for qubit counts or qubit operator weights and can be applied to the investigation of arbitrary fermionic lattice geometries. We showcase our approach by investigating the Fermi-Hubbard model as well as more complex multi-orbital models and report unprecedentedly low circuit depths per Trotter layer.