Fermion lattices can be simulated by same-size qubit lattices with $\mathcal{O}(1)$ interaction overhead

Abstract:Local interactions among electrons underlie many complex properties of correlated materials. While the Jordan-Wigner transformation can preserve this locality along one spatial dimension, interactions along the remaining dimensions typically incur substantial overhead. We show how to simulate all geometrically local interactions on an $N$-site two-dimensional fermion lattice with no asymptotic overhead in the number of interactions and no space overhead. The primary overhead of our method is circuit depth, which on a qubit lattice matches that of fermionic swap networks, scaling as $\mathcal{O}(\sqrt{N})$, but reduces to $\mathcal{O}(\log N)$ on reconfigurable qubit arrays and to $\mathcal{O}(1)$ in lattice-surgery-based surface-code architectures. This is enabled by dynamically reorienting the Jordan-Wigner transformation to switch the lattice dimension along which locality is preserved. Furthermore, we study fermion routing, as required for the simulation of non-local interactions. When using qubit lattices, we reach resource scaling that asymptotically matches that of qubit routing, whilst on fully connected qubit devices, a depth scaling arbitrarily close to $\mathcal{O}(\log N)$ is reached. This allows the fermionic fast Fourier transform to be implemented on qubit lattices with asymptotically optimal resource scaling under these locality constraints. Notably, all of our constructions naturally extend to $d$-dimensional lattices. Beyond scaling improvements, we show explicit examples of our method, including Fermi-Hubbard-model simulations of the square-, Lieb- and kagome lattice and the fermionic fast Fourier transform.

arXiv:2605.12600 [quant-ph]

(or arXiv:2605.12600v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.12600 Focus to learn more arXiv-issued DOI via DataCite

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