Basis-set error bounds for first-quantised quantum simulation of chemistry

Abstract

In quantum simulation of electronic structure it is often expected that the estimate of the ground energy converges to the continuum basis limit at a rate of 𝒪(N⁻¹) for a basis of size N. This has been found in analytical and numerical studies, but without a rigorous treatment of the error in the quantities considered in quantum algorithms. Here we show the 𝒪(N⁻¹) scaling of the error for a wide range of cases needed for quantum simulation of chemistry. We show the error in the ground energy scales as 𝒪(N⁻¹) for plane-wave as well as spatial grid bases. For the spatial grid we consider both a periodic system and a non-periodic system with open boundaries. For time evolution, our bound on the error in the state itself is weaker than 𝒪(N⁻¹), but we show that the error in observables scales as 𝒪̃(N⁻¹) in important cases. In particular, we may consider a smoothed observable that describes the position of particles. We show that this error scales as 𝒪(N^−5/3+tN⁻¹) for time t, again both for plane-wave and spatial grid bases. For the non-periodic grid case we use a condition that the true evolution would not result in significant leakage past the boundaries, which introduces basis error unrelated to the resolution of the discretisation. We also show the error in the kinetic energy of a particle scales as 𝒪((t+log N)/N) for the plane-wave and grid bases. Together, these results show that 𝒪(N⁻¹) scaling of the error holds for many of the relevant cases for quantum algorithms (with a trivial log factor for kinetic energy).

Nonorthogonal variational quantum simulation for quantum chemistry
Zongkang Zhang, Jiajun Ren, Xiao Yuan
arXiv24 Sep 2026PreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
Tensor Networks for Materials Simulation and Quantum Chemistry
Saeed S. Jahromi, Augustine Kshetrimayum, Roman Rausch +2
arXiv23 Oct 2026PreprintarXiv licenceFull textCondensed matterarXiv
Spatial Discretization Error for Quantum Chemistry Simulation
Di Fang, Jiaqi Zhang
arXiv18 Oct 2026PreprintCC BY-NC-ND 4.0Full textMathematical physics Numerical analysis & scientific computingarXiv
Surface chemistry as data for level-set simulation of etching and deposition
Lado Filipovic, Tobias Reiter, Philipp Haslhofer
arXiv1 Nov 2026PreprintCC BY-NC-ND 4.0Full textPhysical chemistry Applied physics & instrumentationarXiv
Realistic Simulation of Valence-band Photoemission Spectra by using First-principles Calculations on the Basis of FLAPW Method
Noriaki Hamada, Satoshi Nakamura, Kenta Takahashi +2
arXiv11 Oct 2026PreprintarXiv licenceFull textCondensed matterarXiv

Cite

BibTeX RIS

BibTeX

@misc{berry2026basisset,
  title = {{Basis-set error bounds for first-quantised quantum simulation of chemistry}},
  author = {Dominic W. Berry and Arkin Tikku and Sophia Simon and Ryan Babbush},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35205},
  eprint = {2610.35205},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35205},
}

RIS

TY  - UNPB
TI  - Basis-set error bounds for first-quantised quantum simulation of chemistry
AU  - Dominic W. Berry
AU  - Arkin Tikku
AU  - Sophia Simon
AU  - Ryan Babbush
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35205
UR  - https://arxiv.org/abs/2610.35205
AB  - In quantum simulation of electronic structure it is often expected that the estimate of the ground energy converges to the continuum basis limit at a rate of 𝒪(N^−1) for a basis of size N. This has been found in analytical and numerical studies, but without a rigorous treatment of the error in the quantities considered in quantum algorithms. Here we show the 𝒪(N^−1) scaling of the error for a wide range of cases needed for quantum simulation of chemistry. We show the error in the ground energy scales as 𝒪(N^−1) for plane-wave as well as spatial grid bases. For the spatial grid we consider both a periodic system and a non-periodic system with open boundaries. For time evolution, our bound on the error in the state itself is weaker than 𝒪(N^−1), but we show that the error in observables scales as 𝒪̃(N^−1) in important cases. In particular, we may consider a smoothed observable that describes the position of particles. We show that this error scales as 𝒪(N^−5/3+tN^−1) for time t, again both for plane-wave and spatial grid bases. For the non-periodic grid case we use a condition that the true evolution would not result in significant leakage past the boundaries, which introduces basis error unrelated to the resolution of the discretisation. We also show the error in the kinetic energy of a particle scales as 𝒪((t+log N)/N) for the plane-wave and grid bases. Together, these results show that 𝒪(N^−1) scaling of the error holds for many of the relevant cases for quantum algorithms (with a trivial log factor for kinetic energy).
ER  -

Abstract

Related

Cite