In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.
In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.
High Resolution Image Download MS PowerPoint Slide We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO 2, and O 2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.
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.
We present an approach that uses the doubly occupied configuration interaction (DOCI) wave function as the trial wave function in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC). DOCI is a seniority-zero method focused on electron pairs. Although DOCI considers much fewer electron configurations than the complete active space (CAS) configuration interaction method, it efficiently captures the static correlation, while the consequent ph-AFQMC recovers the dynamical correlation across all orbitals. We also explore an orbital-optimized version (OO-DOCI) to further improve accuracy. We test this approach on several chemical systems, including single O-H bond breaking in water and polymer additives. In these cases, OO-DOCI-AFQMC closely matches CAS-based ph-AFQMC and even outperforms coupled-cluster singles, doubles, and perturbative triples. However, for strongly correlated systems, such as the carbon dimer and multibond dissociation in hydrogen systems and water, the method's accuracy drops. This suggests that seniority-zero space models may be insufficient as trial wave functions in ph-AFQMC for strongly correlated systems, suggesting the need for trial wave functions in an extended space. Despite such a limitation, our study demonstrates that DOCI- and OO-DOCI-based ph-AFQMC can reduce the steep cost of CAS approaches, offering a path to accurate multireference calculations for larger, more complex systems.
We present an approach that uses the doubly occupied configuration interaction (DOCI) wave function as the trial wave function in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC). DOCI is a seniority-zero method focused on electron pairs. Although DOCI considers much fewer electron configurations than the complete active space (CAS) configuration interaction method, it efficiently captures the static correlation, while the consequent ph-AFQMC recovers the dynamical correlation across all orbitals. We also explore an orbital-optimized version (OO-DOCI) to further improve accuracy. We test this approach on several chemical systems, including single O-H bond breaking in water and polymer additives. In these cases, OO-DOCI-AFQMC closely matches CAS-based ph-AFQMC and even outperforms coupled-cluster singles, doubles, and perturbative triples. However, for strongly correlated systems, such as the carbon dimer and multi-bond dissociation in hydrogen systems and water, the method's accuracy drops. This suggests that seniority-zero space models may be insufficient as trial wave functions in ph-AFQMC for strongly correlated systems, suggesting the need for trial wave functions in an extended space. Despite such a limitation, our study demonstrates that DOCI- and OO-DOCI-based ph-AFQMC can reduce the steep cost of CAS approaches, offering a path to accurate multi-reference calculations for larger, more complex systems.
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.
We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advances, geared toward optimizing computational performance for longer configuration interaction expansions, allow us to use up to a million configurations in the trial state for ph-AFQMC. In one example, we found the cost of ph-AFQMC per sample to increase only by a factor of about 3 for a calculation with 104 configurations compared to that with a single one, demonstrating the tiny computational overhead due to a longer expansion. This favorable scaling allows us to study the systematic convergence of the phaseless bias in auxiliary field quantum Monte Carlo calculations with an increasing number of configurations and provides a means to gauge the accuracy of ph-AFQMC with other trial states. We also show how the scalability issues of sCI trial states for large system sizes could be mitigated by restricting them to a moderately sized orbital active space and leveraging the near-cancellation of out of active space phaseless errors.