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Orbital-rotated Fermi-Hubbard model as a benchmarking problem for quantum chemistry with the exact solution
Ryota Kojima, Masahiko Kamoshita, Keita Kanno
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Quantum chemistry is a key target for quantum computing, but benchmarking quantum algorithms for large molecular systems remains challenging due to the lack of exactly solvable yet structurally realistic models. In particular, molecular Hamiltonians typically contain O(N⁴) Pauli terms, significantly increasing the cost of quantum simulations, while many exactly solvable models, such as the one-dimensional Fermi-Hubbard (1D FH) model, contain only O(N) terms. In this work, we introduce the orbital-rotated Fermi-Hubbard (ORFH) model as a scalable and exactly solvable benchmarking problem for quantum chemistry algorithms. Starting from the 1D FH model, we apply a spin-involved orbital rotation to construct a Hamiltonian that retains the exact ground-state energy but exhibits a Pauli term count scaling as O(N⁴), similar to real molecular systems. We analyze the ORFH Hamiltonian from multiple perspectives, including operator norm and electronic correlation. We benchmark variational quantum eigensolver (VQE) optimizers and Pauli term grouping methods, and compare their performance with those for hydrogen chains. Furthermore, we show that the ORFH Hamiltonian increases the computational difficulty for classical methods such as the density matrix renormalization group (DMRG), offering a nontrivial benchmark beyond quantum algorithms. Our results demonstrate that the ORFH model provides a versatile and scalable testbed for benchmarking quantum chemistry algorithms under realistic structural conditions, while maintaining exact solvability even at large system sizes.
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