  Evaluating the relative performance of different quantum algorithms for
quantum computers is of great significance in the research of quantum
algorithms. In this study, we consider the problem of quantum chemistry, which
is considered one of the important applications of quantum algorithms. While
evaluating these algorithms in systems with a large number of qubits is
essential to see the scalability of the algorithms, the solvable models usually
used for such evaluations typically have a small number of terms compared to
the molecular Hamiltonians used in quantum chemistry. The large number of terms
in molecular Hamiltonians is a major bottleneck when applying quantum
algorithms to quantum chemistry. Various methods are being considered to
address this problem, highlighting its importance in developing quantum
algorithms for quantum chemistry. Based on these points, a solvable model with
a number of terms comparable to the molecular Hamiltonian is essential to
evaluate the performance of such algorithms. In this paper, we propose a set of
exactly solvable Hamiltonians that has a comparable order of terms with
molecular Hamiltonians by applying a spin-involving orbital rotation to the
one-dimensional Fermi-Hubbard Hamiltonian. We verify its similarity to the
molecular Hamiltonian from some prospectives and investigate whether the
difficulty of calculating the ground-state energy changes before and after
orbital rotation by applying the density matrix renormalization group up to 24
sites corresponding to 48 qubits. This proposal would enable proper evaluation
of the performance of quantum algorithms for quantum chemistry, serving as a
guiding framework for algorithm development.
