Mapping of Fermionic Lattice Models for Ising Solvers

TL;DR

This paper introduces a comprehensive pipeline that transforms fermionic and quantum-spin models into annealer-compatible QUBOs, enabling practical quantum simulations with preserved physical properties and validated across various models and hardware.

Contribution

The authors develop a symmetry-aware, end-to-end method for converting complex quantum models into Ising form suitable for annealers, improving accuracy and resource efficiency over previous approaches.

Findings

Successfully reproduces phase transitions in D-Wave hardware.

Achieves ED-level energies for 1D fermionic models.

Demonstrates error reduction with increased replication factor.

Abstract

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-local to 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 2x2 cluster tracking ED slopes up to a uniform offset. A replication-factor study quantifies the accuracy-overhead trade-off, with order-of-magnitude error reduction 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.