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This research establishes fundamental limits on the efficiency of Cartan-based fast-forwarding methods when simulating qubit-mapped fermion models like the Hubbard and Anderson impurity models. By proving that Hamiltonian algebra dimensions scale exponentially with system size, the study demonstrates that these specific quantum chemistry problems cannot be efficiently simulated using current fast-forwarding techniques under standard Majorana-to-Pauli mappings. The findings provide critical theoretical constraints for quantum algorithm design in materials science and condensed matter physics applications.
Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition
arXiv:2502.04620v2 Announce Type: replace Abstract: We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.
Abstract:We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.
arXiv:2502.04620 [quant-ph]
(or arXiv:2502.04620v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2502.04620 Focus to learn more arXiv-issued DOI via DataCite
Phys. Rev. Research 8, 033251 (2026)
https://doi.org/10.1103/zzry-8h81 Focus to learn more DOI(s) linking to related resources
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