Abstract

First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and the two-body Coulomb term achieve quadratic scaling, rather than usual quartic scaling in orbital-based approaches. However, existing schemes employ uniform discretizations whose resolution is imposed by the electron‑nuclear cusps of the wave functions in high‑density regions, thereby oversampling low-density regions and wasting computational resources. To address this, we repurpose the non‑uniform, molecule‑adaptive grids long used for DFT integration, which concentrate points where the electronic density is highest, to discretize the molecular Hamiltonian. Once encoded as a quantum operation, its ground state can be obtained with standard Quantum Phase Estimation. We further derive a transcorrelated, non‑Hermitian yet isospectral Hamiltonian that removes Coulomb singularities and associated cusps in its eigenfunctions, whose ground‑state energy is accessible through the recent generalized Quantum Eigenvalue Estimation protocol. Numerical validation on benchmark systems confirms this ab initio framework paves a promising route to ground‑state chemistry on quantum hardware.