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International Journal of Quantum Chemistry

Evolutionary algorithm based configuration interaction approach

Rahul Chakraborty, Paulami Ghosh, Debashree Ghosh

Published Oct 10, 2017• 18 citations
Publisher

Abstract

Abstract A new evolutionary algorithm for stochastic configuration interaction (CI) method designed as an affordable approximation to full configuration interaction (FCI) has been described here. The key components of the algorithm are initiation, propagation, and termination steps taking inspiration from the genetic algorithm. The propagation step is performed with cloning (retention of a Slater determinant without change), mutation (single excitation/de‐excitation), and crossover (exchange of α and β strings between two Slater determinants) and termination is selection of few Slater determinants based on certain fitness function (measure of importance of a determinant in the CI space) and rejection of the rest. We find that the absolute value of the CI coefficients is a suitable fitness function when combined with a fixed selection scheme. We have tested its accuracy in 1D Hubbard problem and ground state potential energy surface (PES) has also been constructed for symmetric bond breaking of water molecule, where the errors are found to be around 10 mEh with low non‐parallelity error, when retaining only a small fraction of the total number of Slater determinants in the final population. This shows that this method has the ability to capture both static and dynamic correlation. Performance and convergence properties of the algorithm are also tested for N2 triple bond breaking problem. The algorithm opens up a promising way for stochastic sampling of the important determinants in the full Hilbert space.

DOI
10.1002/qua.25509

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Abstract A new evolutionary algorithm for stochastic configuration interaction (CI) method designed as an affordable approximation to full configuration interaction (FCI) has been described here. The key components of the algorithm are initiation, propagation, and termination steps taking inspiration from the genetic algorithm. The propagation step is performed with cloning (retention of a Slater determinant without change), mutation (single excitation/de‐excitation), and crossover (exchange of α and β strings between two Slater determinants) and termination is selection of few Slater determinants based on certain fitness function (measure of importance of a determinant in the CI space) and rejection of the rest. We find that the absolute value of the CI coefficients is a suitable fitness function when combined with a fixed selection scheme. We have tested its accuracy in 1D Hubbard problem and ground state potential energy surface (PES) has also been constructed for symmetric bond breaking of water molecule, where the errors are found to be around 10 mEh with low non‐parallelity error, when retaining only a small fraction of the total number of Slater determinants in the final population. This shows that this method has the ability to capture both static and dynamic correlation. Performance and convergence properties of the algorithm are also tested for N2 triple bond breaking problem. The algorithm opens up a promising way for stochastic sampling of the important determinants in the full Hilbert space.
A stochastic configuration interaction method based on evolutionary algorithm is designed as an affordable approximation to full configuration interaction (FCI). The algorithm comprises of initiation, propagation and termination steps, where the propagation step is performed with cloning, mutation and cross-over, taking inspiration from genetic algorithm. We have tested its accuracy in 1D Hubbard problem and a molecular system (symmetric bond breaking of water molecule). We have tested two different fitness functions based on energy of the determinants and the CI coefficients of determinants. We find that the absolute value of CI coefficients is a more suitable fitness function when combined with a fixed selection scheme.
High Resolution Image Download MS PowerPoint Slide Selected Configuration Interaction (SCI) is a method in molecular electronic structure theory that allows for the construction of configuration subspaces adapted to the particular system under study. This adaptability is achieved by guiding subspace construction with respect to a selection criterion designed to identify and retain the most important configurations for an accurate description of the system. Quantum-SCI (QSCI) introduces quantum resources to inform the construction of these subspaces, motivated by the classical hardness of state sampling and system dynamics. As with conventional SCI, the CI routine is still performed classically and is therefore not corrupted by hardware noise; only the subspace quality is affected by deficiencies in the quantum hardware. Previous QSCI approaches take the measurements produced by a physically motivated circuit construction, often with a recovery step to mitigate against errors, and form a subspace from the resulting configurations. We propose an alternative approach that is more aligned with conventional selection criteria but attempts to inject classically inaccessible information into the selection step with the aim of enabling new subspace expansion pathways. The approach presented in this work uses the population statistics of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure. Importantly, this occupancy-guided expansion complements rather than replaces the direct inclusion of valid configurations sampled from the time-evolved quantum state, so determinants containing higher-order excitations can still enter the variational space in a single iteration. We also include multireference perturbation theory to capture missed correlations outside the configuration subspace. This is demonstrated on hardware by using 42 qubits of an IQM superconducting device to compute the potential energy curve of SiH 4 in a 6-31G basis set as the Si–H bonds are stretched. We benchmark against the best-in-class Heatbath CI algorithm to assess the compactness of the resulting wave function.
We provide a very simple adaptation of our recently published quantum Monte Carlo algorithm in full configuration-interaction (Slater determinant) spaces which dramatically reduces the number of walkers required to achieve convergence. A survival criterion is imposed for newly spawned walkers. We define a set of initiator determinants such that progeny of walkers spawned from such determinants onto unoccupied determinants are able to survive, while the progeny of walkers not in this set can survive only if they are spawned onto determinants which are already occupied. The set of initiators is originally defined to be all determinants constructable from a subset of orbitals, in analogy with complete-active spaces. This set is dynamically updated so that if a noninitiator determinant reaches an occupation larger than a preset limit, it becomes an initiator. The new algorithm allows sign-coherent sampling of the FCI space to be achieved with relatively few walkers. Using the N(2) molecule as an illustration, we show that rather small initiator spaces and numbers of walkers can converge with submilliHartree accuracy to the known full configuration-interaction (FCI) energy (in the cc-pVDZ basis), in both the equilibrium geometry and the multiconfigurational stretched case. We use the same method to compute the energy with cc-pVTZ and cc-pVQZ basis sets, the latter having an FCI space of over 10(15) with very modest computational resources.
In this work, we introduce a perturbative Selective Configuration Interaction (SCI) approach guided by a binary machine-learning classifier. The method leverages a lightweight feedforward neural network (FNN), purposefully designed for fast and efficient training. Within this framework, we show that our model attains the accuracy of the state-of-the-art SCI method CIPSI (Configuration Interaction using a Perturbative Selection done Iteratively). Across all tested configuration-space sizes, our approach reliably identifies the most important Slater determinants using a binary cross-entropy metric, achieving FCI/CASCI-level accuracy within 10 –4 Hartree for both ground and excited states. Finally, the method remains robust for strained geometries and conformational changes, successfully classifying Slater determinants across multiple points of potential energy curves and surfaces. This capability opens the door to new regression-based strategies for molecular electronic structure and the construction of machine-learning-driven potential energy surfaces.
We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces. The new method is a population dynamics of a set of walkers, and is designed to simulate the underlying imaginary-time Schrödinger equation of the interacting Hamiltonian. The walkers (which carry a positive or negative sign) inhabit Slater determinant space, and evolve according to a simple set of rules which include spawning, death and annihilation processes. We show that this method is capable of converging onto the full configuration-interaction (FCI) energy and wave function of the problem, without any a priori information regarding the nodal structure of the wave function being provided. Walker annihilation is shown to play a key role. The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. At this point, the correlation energy can be measured using two independent methods--a projection formula and a energy shift; agreement between these provides a strong measure of confidence in the accuracy of the computed correlation energies. We have verified the method by performing calculations on systems for which FCI calculations already exist. In addition, we report on a number of new systems, including CO, O(2), CH(4), and NaH--with FCI spaces ranging from 10(9) to 10(14), whose FCI energies we compute using modest computational resources.
Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many-particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: (1) modified Hubbard model with different inter- and intracluster hopping terms, (2) less obviously clusterable cases of bond breaking in N 2 and F 2, and (3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.