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Size-consistent implementation of Hamiltonian simulation-based quantum-selected configuration interaction method for the supramolecular approach

Kenji Sugisaki

TL;DR

This work tackles the lack of size consistency in quantum-selected configuration interaction (QSCI) by introducing a size-consistent implementation (sc-HSB-QSCI) that samples the dimer in localized molecular orbitals and constructs monomer and dimer subspaces with a symmetry-completion step to include missing determinants. The method ensures size consistency across multi-monomer systems and demonstrates zero intermolecular energy errors at large separations, while achieving CAS-CI accuracy (within ~0.04 kcal/mol) for hydrogen-bonded dimers. The approach is demonstrated on 4H/8H/12H clusters, FH dimer, and FH--H$_2$O, with comparisons to supramolecular and dimer strategies showing favorable accuracy and scalability. These results indicate sc-HSB-QSCI as a practical path for accurate intermolecular energies on near-term quantum hardware, with potential extensions to other selected-CI frameworks and orbital localization enhancements.

Abstract

The quantum-selected configuration interaction (QSCI) method is a promising approach for large-scale quantum chemical calculations on currently available quantum hardware. However, its naive implementation lacks size consistency, which is essential for accurate intermolecular interaction energy calculations using the supramolecular approach. Here, we present a size-consistent implementation of QSCI by sampling Slater determinants for the dimer in the localized molecular orbital basis, constructing the subspaces for the monomers and dimer, and augmenting the dimer subspace with additional determinants required for size consistency. Implemented within the Hamiltonian simulation-based QSCI (HSB-QSCI) framework, our method numerically satisfies size consistency for 4H/8H/12H clusters, the FH dimer, and the FH--H$_2$O system. Application to intermolecular interaction energy calculations of hydrogen-bonded FH dimer and FH--H$_2$O demonstrates that our approach reproduces complete active space-configuration interaction (CAS-CI) values with errors below 0.04 kcal mol$^{-1}$.

Size-consistent implementation of Hamiltonian simulation-based quantum-selected configuration interaction method for the supramolecular approach

TL;DR

This work tackles the lack of size consistency in quantum-selected configuration interaction (QSCI) by introducing a size-consistent implementation (sc-HSB-QSCI) that samples the dimer in localized molecular orbitals and constructs monomer and dimer subspaces with a symmetry-completion step to include missing determinants. The method ensures size consistency across multi-monomer systems and demonstrates zero intermolecular energy errors at large separations, while achieving CAS-CI accuracy (within ~0.04 kcal/mol) for hydrogen-bonded dimers. The approach is demonstrated on 4H/8H/12H clusters, FH dimer, and FH--HO, with comparisons to supramolecular and dimer strategies showing favorable accuracy and scalability. These results indicate sc-HSB-QSCI as a practical path for accurate intermolecular energies on near-term quantum hardware, with potential extensions to other selected-CI frameworks and orbital localization enhancements.

Abstract

The quantum-selected configuration interaction (QSCI) method is a promising approach for large-scale quantum chemical calculations on currently available quantum hardware. However, its naive implementation lacks size consistency, which is essential for accurate intermolecular interaction energy calculations using the supramolecular approach. Here, we present a size-consistent implementation of QSCI by sampling Slater determinants for the dimer in the localized molecular orbital basis, constructing the subspaces for the monomers and dimer, and augmenting the dimer subspace with additional determinants required for size consistency. Implemented within the Hamiltonian simulation-based QSCI (HSB-QSCI) framework, our method numerically satisfies size consistency for 4H/8H/12H clusters, the FH dimer, and the FH--HO system. Application to intermolecular interaction energy calculations of hydrogen-bonded FH dimer and FH--HO demonstrates that our approach reproduces complete active space-configuration interaction (CAS-CI) values with errors below 0.04 kcal mol.
Paper Structure (13 sections, 8 equations, 4 figures, 12 tables)

This paper contains 13 sections, 8 equations, 4 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Quantum computational approaches for intermolecular interaction energy calculations
  3. Theory
  4. Computational conditions
  5. Results and Discussion
  6. Size consistency of sc-HSB-QSCI
  7. Intermolecular interaction energies of hydrogen-bonded FH dimer and FH--H$_2$O
  8. Conclusion
  9. Acknowledgments
  10. Supporting Information
  11. Cartesian coordinates
  12. Relationship between the number of quantum circuit repetitions and size consistency
  13. Size-consistent implementation for heat-bath CI

Figures (4)

  • Figure 1: Schematic illustration of subspace generation in sc-HSB-QSCI. $|\Phi_\text{Di}\rangle$ represents an approximate wave function for the dimer, and $U$ is a time evolution operator $U = e^{-iHt}$.
  • Figure 2: PBE0/aug-cc-pVDZ optimized geometry of the FH dimer and FH--H$_2$O. Red dotted lines represent hydrogen bonds, and values in red denote intermolecular distances in units of Å.
  • Figure S1: Number of dimer Slater determinants included in the subspace Hamiltonian versus intermolecular interaction energy obtained from sc-HCI and sc-HSB-QSCI in (a) FH dimer and in (b) FH--H$_2$O.
  • Figure S2: Localized molecular orbitals of FH dimer and FH--H$_2$O used as active space for HSB-QSCI. Orbitals with yellow highlights are occupied ones, and those without highlight are unoccupied.