Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension

TL;DR

This paper introduces a novel quantum chemistry algorithm using adaptive, non-uniform grids and transcorrelated methods to efficiently and accurately compute molecular ground states on quantum computers, reducing resource waste.

Contribution

It presents a new non-uniform grid approach combined with transcorrelated Hamiltonians for quantum chemistry, improving efficiency and accuracy over uniform discretization schemes.

Findings

Adaptive grids focus computational resources on high-density regions.

Transcorrelated Hamiltonians eliminate Coulomb singularities.

Numerical validation shows promising accuracy for ground-state calculations.

Abstract

First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling of two-electron interactions. However, existing schemes employ uniform discretizations, so the resolution required to capture electron-nuclear cusps in high-density regions oversamples low-density regions, wasting computational resources. We address this by deploying non-uniform, molecule-adaptive grids that concentrate points where electronic density is high. Using Voronoi partitions of these grids, the molecular Hamiltonian is expressed in a Hermitian form and in a transcorrelated, isospectral form that eliminates Coulomb singularities and yields cusp-free eigenfunctions. Both formulations slot naturally into quantum eigenvalue solvers: Hermitian Quantum Phase Estimation (QPE) and the recent generalised Quantum Eigenvalue Estimation (QEVE) protocol for its non-Hermitian, transcorrelated counterpart. Numerical validation on benchmark systems confirms that this non-heuristic ab initio framework offers a promising path for accurate ground-state chemistry on quantum hardware.