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This study evaluates the impact of molecular orbital localization on the computational resources required for Hamiltonian simulation in one-dimensional hydrogen chain systems, comparing Hartree鈥揊ock canonical molecular orbitals (CMOs) and Pipek鈥揗ezey-based localized molecular orbitals (LMOs). The findings reveal that while CMO-based expansions benefit from a threshold on Hamiltonian coefficients to reduce gate costs, LMO-based expansions achieve superior efficiency through operator locality-based Hamiltonian truncation. Notably, the research demonstrates that the number of quantum gates needed for simulation grows polynomially with CMOs but only polylogarithmically with LMOs, indicating a significant advantage for the latter in scaling to larger systems.
LMO-based wave function expansions can reduce quantum gate requirements for Hamiltonian simulations from polynomial to polylogarithmic growth, offering a game-changing efficiency boost for large-scale quantum simulations.
We investigate how molecular orbitals used as the basis of wave function expansion and how operator coefficient-based and locality-based Hamiltonian truncation affects the computational cost of Trotter decomposition-based Hamiltonian simulation in one-dimensional hydrogen chain systems. The analysis is performed using both Hartree--Fock canonical molecular orbitals (CMOs) and Pipek--Mezey-based localized molecular orbitals (LMOs). For short hydrogen chains, we evaluate the ground-state energy and fidelity and find that, in the CMO-based wave function expansion, introducing a threshold on Hamiltonian coefficients is effective in reducing the gate cost while maintaining computational accuracy. In contrast, in the LMO-based wave function expansion, operator locality-based Hamiltonian truncation is found to be more effective. By fitting the relationship between the truncation threshold and the ground-state energies and fidelities with empirical formulas, we estimate the threshold values required to achieve high fidelity ($F \ge 0.99$) in the ground-state wave function. Using the estimated thresholds, we then perform quantum gate resource estimation for longer hydrogen chains up to H$_{100}$. The results suggest an exponential advantage of the LMO-based wave function expansion with Hamiltonian truncation: the number of quantum gates required for Hamiltonian simulation grows polynomially when the CMO-based wave function expansion with operator coefficient-based Hamiltonian truncation is adopted, whereas it grows polylogarithmically when the LMO-based wave function expansion is combined with operator locality-based Hamiltonian truncation. These results provide useful guidelines for choosing orbital representations and Hamiltonian truncation strategies in large-scale quantum chemical simulations.
