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arXiv:2605.11257

Size Extensive Auxiliary-Field Quantum Monte Carlo with Perturbative Coupled Cluster Trial Wavefunction

Yichi Zhang, Ankit Mahajan, Yann Damour, Sandeep Sharma

Published May 11, 2026• 0 citations
arXivHTMLPDF

Abstract

In this work, we develop a size extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as $O(N^5)$ for local energy evaluation by treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions perturbatively. Comprehensive numerical examinations, spanning from main-group molecules to $3d$ transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles (CISD) trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas (UEG) provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit (TDL).

DOI
10.48550/arxiv.2605.11257

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In this work, we develop a size extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as O(N5)O(N^5)O(N5) for local energy evaluation by treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions perturbatively. Comprehensive numerical examinations, spanning from main-group molecules to 3d3d3d transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles (CISD) trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas (UEG) provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit (TDL).
In this work, we develop a size-extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as O(N5) for local energy evaluation by perturbatively treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions. Comprehensive numerical examinations, spanning from main-group molecules to 3d transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit.
We introduce a black-box auxiliary field quantum Monte Carlo (AFQMC) approach to perform highly accurate electronic structure calculations using configuration interaction singles and doubles (CISD) trial states. This method consistently provides more accurate energy estimates than coupled cluster singles and doubles with perturbative triples (CCSD(T)), often regarded as the gold standard in quantum chemistry. This level of precision is achieved at a lower asymptotic computational cost, scaling as O ( N 6 ) compared to the O ( N 7 ) scaling of CCSD(T). We provide numerical evidence supporting these findings through results for challenging main group and transition metal-containing molecules.
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We systematically investigate the calculation of excited states in quantum chemistry using auxiliary field quantum Monte Carlo (AFQMC). Symmetry allows targeting of the lowest triplet excited states in AFQMC based on restricted open-shell determinants, effectively as a ground-state calculation. For open-shell singlet states, excited-state calculations can be stabilized with the appropriate trial states, but their quality can have a larger effect on the accuracy in AFQMC. We find that active space-based configuration interaction trial states are often not sufficient to obtain accurate results. We instead use truncated equation of motion coupled cluster with single and double excitations (EOM-CCSD) as trial states. We benchmark the performance of these calculations on a set of small and medium molecules and polyacenes, focusing on predominantly single excitations. We find that the AFQMC results, obtained at a per-sample cost scaling of O(N6), are systematically more accurate than those obtained using EOM-CCSD, reducing excitation energy errors by approximately half for open-shell singlets. In regimes where EOM-CC triples are impractical, these results position AFQMC as a scalable, higher-accuracy complement for low-lying excited states.
to develop quantum Monte Carlo (QMC) approaches for excited states and for more systematic and accurate treatment of ground states of strongly correlated sytems and heavier elements. We use the auxiliary-field quantum Monte Carlo (AFQMC) framework, which is a many-body total energy method that looks like many coupled mean-field calculations. I will discuss this method’s relations and dierences with traditional density-functional and quantum chemistry methods, and with other forms of QMC. The AFQMC method uses importance-sampled random walks in the space of nonorthogonal Slater determinants to project out the many-body ground state, or excited state. The random walks are constrained by a trial wave function (TWF) to remove the so-called sign problem, giving approximate (but non-perturbative) results. With singledeterminant TWFs from Hartree-Fock or density-functional theory (DFT), this approach can be thought of as a post-DFT method with no parameter. In this form, the accuracy is typically comparable to the quantum chemistry coupled-cluster CCSD(T) method near equilibrium geometries, and better than CCSD(T) when bonds are stretched. The computational cost of AFQMC scales as N 3 with characteristic size of the system. Its accuracy can be further improved at the cost of increased computing (releasing the constraint) or better TWF. With AFQMC, we can systematically target selected orbitals to correlate. This allows many-body calculations in solids with a frozen core, with down-folded Hamiltonians, or possibly embeded in a DFT calculations to extend scales. Results from a few on-going applications will be presented, including band structures in simple solids, magnetic phases in MnO, and Cobalt adsoption on graphene.
The phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method is a stochastic imaginary-time projection method for computing ground-state properties of strongly correlated quantum systems, whose accuracy depends critically on the trial wavefunction. We present a benchmarking study of trial wavefunctions prepared using parameterized quantum circuits, spanning unitary coupled cluster (UCC), Hamiltonian-informed, Jastrow-inspired, and adaptively constructed ansatzes, and evaluate their accuracy, expressibility, and resource requirements within the quantum-computing-enhanced AFQMC (QC-AFQMC) framework. Trial states are prepared with GPU-accelerated statevector simulations using CUDA-Q and tested on stretched linear hydrogen chains and nine closed-shell molecules at equilibrium with varying static correlation. We find that at similar parameter counts, ph-AFQMC largely removes differences between families for weakly and moderately correlated systems: every trial yields a ph-AFQMC energy within chemical accuracy despite trial energy errors spanning nearly three orders of magnitude, whereas ansatz choice becomes consequential as static correlation grows. Our results indicate that trial variational energy is not always a reliable indicator of ph-AFQMC quality, and that adding variational parameters can lower the trial energy while degrading the ph-AFQMC energy. Across our benchmark systems, trial fidelity ranks trials more reliably than variational energy, and for spin-contaminated trials, the singlet-projected fidelity is more reliable than unprojected fidelity. The UCCSD ansatz initialized from unrestricted CCSD amplitudes provides a robust and inexpensive-to-optimize baseline across benchmark systems, with circuit depth as its principal limitation, while adaptive and compact layered ansatzes remain competitive in accuracy under strong correlation with substantially shallower circuits.