Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction

The Green's function coupled cluster (GFCC) method is a powerful many-body tool for computing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, for the GFCC to be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its high computational overhead. In our recent studies, we demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly, for a frequency regime which requires high resolution spectral function, instead of solving GFCC linear equation of full dimension for every single frequency point, an efficiently-solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace and the linear system model can be systematically improved. The method is tested in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. As a byproduct, the obtained reduced order model may provide a high quality initial guess which improves the convergence rate for the existing iterative linear solver.Comment: 29 pages, 8 figure

Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory

With growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schr\"odinger equation is of keen interest in modern electronic structure theory. In the present work, we present two novel approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory (TD-EOM-CC) based on the Chebyshev and Arnoldi expansions of the complex, non-hermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper, et al [J. Phys. Chem. A. 2021 125, 5438-5447], the fourth-order Runge-Kutta method (RK4), and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.Comment: 28 pages, 4 figure

A Parallel, Distributed Memory Implementation of the Adaptive Sampling Configuration Interaction Method

Many-body simulations of quantum systems is an active field of research that involves many different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing.Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However development of sCI methods targeting massively parallel resources has been explored only in a few research works. In this work, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. Presented benchmarks demonstrate parallel efficiency exceeding 95\% for the variational ASCI calculation of Cr$_2$ (24e,30o) with $10^6, 10^7$, and $3*10^8$ variational determinants up to 16,384 CPUs. To the best of the authors' knowledge, this is the largest variational ASCI calculation to date.Comment: 32 pages, 4 figure

On the Efficient Evaluation of the Exchange Correlation Potential on Graphics Processing Unit Clusters

The predominance of Kohn-Sham density functional theory (KS-DFT) for the theoretical treatment of large experimentally relevant systems in molecular chemistry and materials science relies primarily on the existence of efficient software implementations which are capable of leveraging the latest advances in modern high performance computing (HPC). With recent trends in HPC leading towards in increasing reliance on heterogeneous accelerator based architectures such as graphics processing units (GPU), existing code bases must embrace these architectural advances to maintain the high-levels of performance which have come to be expected for these methods. In this work, we purpose a three-level parallelism scheme for the distributed numerical integration of the exchange-correlation (XC) potential in the Gaussian basis set discretization of the Kohn-Sham equations on large computing clusters consisting of multiple GPUs per compute node. In addition, we purpose and demonstrate the efficacy of the use of batched kernels, including batched level-3 BLAS operations, in achieving high-levels of performance on the GPU. We demonstrate the performance and scalability of the implementation of the purposed method in the NWChemEx software package by comparing to the existing scalable CPU XC integration in NWChem.Comment: 26 pages, 9 figure

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems

Accurate Assignments of Excited-State Resonance Raman Spectra: A Benchmark Study Combining Experiment and Theory

This is an unofficial translation of an article that appeared in an ACS publication. ACS has not endorsed the content of this translation or the context of its use.Femtosecond stimulated Raman scattering (FSRS) probes the structural dynamics of molecules in electronically excited states by following the evolution of the vibrational spectrum. Interpreting the dynamics requires accurate assignments to connect the vibrational bands with specific nuclear motions of an excited molecule. However, the assignment of FSRS signals is often complicated by mode-specific resonance enhancement effects that are difficult to calculate for molecules in electronically excited states. We present benchmark results for a series of eight aryl-substituted thiophene derivatives to show that calculated off-resonance Raman spectra can be used to assign experimental bands on the basis of a comparison of structurally similar compounds and careful consideration of the resonance condition. Importantly, we show that direct comparison with the off-resonant calculations can lead to incorrect assignments of the experimental spectrum if the resonance condition is neglected. These results highlight the importance of resonance enhancement effects in assigning FSRS spectra

Distributed Memory, GPU Accelerated Fock Construction for Hybrid, Gaussian Basis Density Functional Theory

With the growing reliance of modern supercomputers on accelerator-based architectures such a GPUs, the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development of GPU accelerated, distributed memory algorithms for many-body (e.g. coupled-cluster) and spectral single-body (e.g. planewave, real-space and finite-element density functional theory [DFT]), the vast majority of GPU-accelerated Gaussian atomic orbital methods have focused on shared memory systems with only a handful of examples pursuing massive parallelism on distributed memory GPU architectures. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact-exchange matrices for hybrid Kohn-Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.Comment: 45 pages, 9 figure

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physics and chemistry is one of the most promising applications of quantum computing. In this paper, we introduce a novel measurement-driven approach that finds eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). We provide theoretical and numerical evidence that our method converges rapidly even in the presence of noise and show that our method is isomorphic to matrix pencil methods developed independently across various scientific communities. Our DMD-based strategy can systematically mitigate perturbative noise and stands out as a promising hybrid quantum-classical eigensolver