Differentiated Determinant Graphs Enable Large-Scale Multideterminant Auxiliary-Field Quantum Monte Carlo
Abstract
Multideterminant trial wave functions can reduce phaseless bias in auxiliary-field quantum Monte Carlo (AFQMC), but the repeated evaluation of their overlap, force bias, and local energy restricts systematic trial improvement. In this work, we organize particle--hole excitation determinants as a shared arithmetic directed acyclic graph of canonical minors. A coefficient-weighted reverse pass and batched directional passes evaluate the complete estimator without determinant-resolved cofactor tensors while preserving the sparse α--β coefficient coupling exactly. Controlled complex-valued tests verify the complete kernel to machine precision and show orders-of-magnitude acceleration over direct determinant summation. In molecular calculations, the observed cost remains sublinear through million-configuration selected-CI trials and the same estimator remains usable at one hundred million configurations, where the eventual exact coefficient-contraction boundary becomes visible. For Cr2, an orbital-optimized CAS(12e,42o) trial in a double-ζ basis yields a potential-energy curve (PEC) and spectroscopic constants in close agreement with experiment. Differentiated determinant graphs therefore convert very large correlated trials from a formal accuracy hierarchy into a practical route for systematic AFQMC studies of strongly correlated molecules.
Related
- Open-shell Configuration State Functions as trial states for phaseless auxiliary-field quantum Monte Carlo
- Accelerated Quantum-Assisted Selected Configuration Interaction via Fast-Annealing-Based Determinant Selection
- Tuning Luminescent Thermometry in Ytterbium N3O2 Field-Induced Single-Molecule Magnets via Auxiliary Ligands.
- Development of a Minimal Auxiliary Basis for the Particle--Particle Random Phase Approximation (ppRPA): Accelerating Excited-State Calculations in Diradical Nanoparticles and Periodic Systems
- Molecular Conformation as a Determinant of Self-Assembly in Sequence-Isomeric Tripeptides.
BibTeX
@misc{williams2026differentiated,
title = {{Differentiated Determinant Graphs Enable Large-Scale Multideterminant Auxiliary-Field Quantum Monte Carlo}},
author = {Jacob Z. Williams and Yu Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29851},
eprint = {2610.29851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29851},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Differentiated Determinant Graphs Enable Large-Scale Multideterminant Auxiliary-Field Quantum Monte Carlo
AU - Jacob Z. Williams
AU - Yu Zhang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29851
UR - https://arxiv.org/abs/2610.29851
AB - Multideterminant trial wave functions can reduce phaseless bias in auxiliary-field quantum Monte Carlo (AFQMC), but the repeated evaluation of their overlap, force bias, and local energy restricts systematic trial improvement. In this work, we organize particle--hole excitation determinants as a shared arithmetic directed acyclic graph of canonical minors. A coefficient-weighted reverse pass and batched directional passes evaluate the complete estimator without determinant-resolved cofactor tensors while preserving the sparse α--β coefficient coupling exactly. Controlled complex-valued tests verify the complete kernel to machine precision and show orders-of-magnitude acceleration over direct determinant summation. In molecular calculations, the observed cost remains sublinear through million-configuration selected-CI trials and the same estimator remains usable at one hundred million configurations, where the eventual exact coefficient-contraction boundary becomes visible. For Cr_2, an orbital-optimized CAS(12e,42o) trial in a double-ζ basis yields a potential-energy curve (PEC) and spectroscopic constants in close agreement with experiment. Differentiated determinant graphs therefore convert very large correlated trials from a formal accuracy hierarchy into a practical route for systematic AFQMC studies of strongly correlated molecules.
ER -