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

• URL: http://arxiv.org/abs/2507.20583v1
• Date: Mon, 28 Jul 2025 07:35:52 GMT
• Title: Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension
• Authors: César Feniou, Christopher Cherfan, Julien Zylberman, Baptiste Claudon, Jean-Philip Piquemal, Emmanuel Giner,
• Abstract summary: First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing.<n>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.<n>We address this by deploying non-uniform, molecule-adaptive grids that concentrate points where electronic density is high.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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