aiqbench analysis
This research presents a significant algorithmic advancement for real-space quantum chemistry, utilizing adaptive grids and transcorrelated extensions to optimize qubit usage and eliminate Coulomb singularities. By integrating these non-uniform discretizations with Hermitian Quantum Phase Estimation and generalized QEVE protocols, the work offers a more efficient pathway toward accurate ground-state calculations on fault-tolerant quantum hardware.
Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension
arXiv:2507.20583v2 Announce Type: replace 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.
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.
Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)
arXiv:2507.20583 [quant-ph]
(or arXiv:2507.20583v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2507.20583 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1039/D6DD00002A Focus to learn more DOI(s) linking to related resources
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Full text under the publisher's open licence · 254 words
