Quantum Molecular Science III

In the NISQ (Noisy Intermediate-Scale Quantum) era, single-particle basis set engineering is crucial for quantum simulation methods in solving electronic structure problems. While conventional Gaussian basis sets are popular for molecular systems due to their analytical evaluation and compact representation of molecular orbitals, they face challenges when applied to quantum algorithms. Specifically, the electronic Hamiltonians discretized by a Gaussian-orbital basis generally have O(N⁴) non-vanishing terms, with N being the size of the selected basis set. This nonlinear scaling results in an asymptotically high logic gate count that is unrealizable for near-term digital quantum devices. Additionally, the Gaussian basis sets have inconsistent size-to-error ratios across different systems, which poses a challenge for implementing simulation algorithms with limited quantum computational resources.