Investigating Interacting Fermionic Models with Locality-Preserving Qubit Encodings

Simulating strongly correlated fermionic systems on quantum computers is hindered by the nonlocality of standard fermion-to-qubit mappings like the Jordan-Wigner (JW) transformation. In two dimensions, JW mapping causes local fermionic interactions to map to Pauli strings whose weight grows with system size, leading to significant circuit overhead. This paper investigates whether the locality-preserving Derby-Klassen (DK) mapping can mitigate this nonlocality in variational quantum simulations of two-dimensional $t$-$V$ and Fermi-Hubbard models.

The authors employ the DK mapping, which uses auxiliary qubits on lattice faces to preserve the locality of fermionic interactions. Because this mapping enlarges the Hilbert space, the physical fermionic states must be constrained to a specific subspace defined by stabilizer operators. The researchers incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) using Clifford-gate state preparation. This ensures that the variational optimization remains within the physical code space. They benchmark this DK-HVA framework against JW-based circuits, evaluating performance through statevector simulations of various lattice sizes.

The study shows that the DK-HVA framework accurately reproduces the low-energy spectra and physical observables of the $t$-$V$ model. By exploiting particle-number conservation, the authors successfully resolve degenerate low-energy states. Crucially, at finite chemical potential, the DK-HVA demonstrates a clear advantage over the JW mapping: it maintains comparable variational accuracy while requiring significantly lower logical-circuit depth and CNOT counts. The authors also provide an initial extension to the spinful Fermi-Hubbard model, identifying a design tradeoff between fermionic-mode placement and the locality of interaction terms.