Mapping of fermionic lattice models for Ising solvers

We present an end-to-end, symmetry-aware pipeline that converts interacting fermionic and quantum-spin models into annealer-ready QUBOs while preserving low-energy physics. The workflow combines Bravyi–Kitaev encoding, exact Z₂ symmetry tapering, Xia–Bian–Kais (XBK) diagonalization to a Z-only form, and k \!→ \!2 local quadratization, with ground energies recovered via a Dinkelbach fixed-point over the resulting Ising objective. We validate the approach across a complexity ladder: (i) a frustrated 2D Ising model run on a D-Wave Advantage QPU reproduces the known ferromagnet–stripe transition; (ii) finite-temperature checks on 1D Ising recover standard finite-size trends; (iii) a genuinely quantum spin target (XXZ) matches exact diagonalization (ED) on small chains; and (iv) interacting fermions (t–V) in 1D (rings $$L=2\!-\!8$$) show ED-level energies and the expected kink near V/t≈ 2, with a 2D 2× 2 cluster tracking ED slopes up to a uniform offset. A replication-factor study quantifies the accuracy–overhead trade-off, with O-of-magnitude error reduction by and diminishing returns beyond r\!≈ \!Nq Except for the classical Ising benchmark and Molecular benchmarks, experiments use D-Wave’s public DIMOD and Neal simulators; a molecular benzene case in the appendix illustrates portability beyond lattices. The results establish a practical pathway for mapping quantum matter to current annealers, with clear knobs for fidelity, resources, and embedding.