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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2605.12600 |
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| _version_ | 1866916006568394752 |
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| author | Aigner, Gregor Klaver, Berend Lanthaler, Martin Lechner, Wolfgang |
| author_facet | Aigner, Gregor Klaver, Berend Lanthaler, Martin Lechner, Wolfgang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12600 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fermion lattices can be simulated by same-size qubit lattices with $\mathcal{O}(1)$ interaction overhead Aigner, Gregor Klaver, Berend Lanthaler, Martin Lechner, Wolfgang Quantum Physics 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. |
| title | Fermion lattices can be simulated by same-size qubit lattices with $\mathcal{O}(1)$ interaction overhead |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.12600 |