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arXiv:1608.04901

Evolutionary algorithm based configuration interaction approach

Rahul Chakraborty, Debashree Ghosh

Published Aug 17, 2016• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1608.04901

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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.
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.
Accurate quantum chemical calculations are critical for understanding molecular properties, yet their computational cost remains a major challenge. Full Configuration Interaction (FCI) provides exact solutions but is prohibitively expensive for large systems. To address this, quantum computers are expected to be useful, but developing practical quantum computers is still ongoing. Here we introduce an efficient Configuration Interaction (CI) computation algorithm based on classical mechanics, which we call Simulated Bifurcation-based CI (SBCI), because we derive this algorithm from a quantum inspired algorithm for combinatorial optimization called Simulated Bifurcation. Applying it to FCI computations of representative molecular systems and comparing the results with those by a standard method, we demonstrate that SBCI can reduce computation costs such as computation times and/or required memory sizes, while keeping high accuracy comparable to the standard method. Thus, SBCI will be promising for accelerating high-precision electronic structure calculations without compromising reliability.
Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. We explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.
We introduce a family of methods for the full configuration interaction problem in quantum chemistry, based on the fast randomized iteration (FRI) framework [Lim, L.-H.; Weare, J. SIAM Rev. 2017, 59, 547; DOI: 10.1137/15M1040827 ]. These methods, which we term “FCI-FRI”, stochastically impose sparsity during iterations of the power method and can be viewed as a generalization of full configuration interaction quantum Monte Carlo (FCIQMC) without walkers. In addition to the multinomial scheme commonly used to sample excitations in FCIQMC, we present a systematic scheme where excitations are not sampled independently. Performing ground-state calculations on five small molecules at fixed cost, we find that the systematic FCI-FRI scheme is 11–45 times more statistically efficient than the multinomial FCI-FRI scheme, which is in turn 1.4–178 times more statistically efficient than the original FCIQMC algorithm.
To avoid the combinatorial computational cost of configuration interaction (CI), we previously introduced the symmetric tensor decomposition CI (STD-CI) method, which takes advantage of the antisymmetric nature of the electronic wave function and expresses the CI coefficients compactly as a series of Kronecker product states (STD series) [W. Uemura and O. Sugino, Phys. Rev. Lett. 109, 253001 (2012)]. Here we extend the variational degrees of freedom by using different molecular orbitals for different terms in the STD series. This scheme is equivalent to the linear combination of the Hartree-Fock-Bogoliubov state or the antisymmetrized geminal powers (AGPs). The total energy converges very rapidly within 0.72 $\ensuremath{\mu}\mathrm{hartree}$ taking only 10 terms for the water molecule, and the convergence is likewise fast for Hubbard tetramers. The computational cost scales as the fifth power of the number of electrons and the square of the number of terms in the STD series, indicating the promise of this AGP-based scheme for highly accurate and efficient computation of quantum systems.
Machine learning-assisted configuration interaction (MLCI) has been shown earlier as a promising method in determining the electronic structure of the model and molecular Hamiltonians. In the MLCI approach to molecular Hamiltonians, it has been noticed that prediction is strongly dependent on the connectedness of the training and validation spaces. In this work, we have tested three different models with different output parameters (abs-MLCI, transformed-MLCI, and log-MLCI) to verify the robustness of training these models. We define robustness as the extent of error in prediction even when the spaces (training and validation) are not connected. We notice that the log-MLCI model is best suited to this approach and is therefore a powerful model for accurate one-shot variational energies. This is tested for chemical bond breaking in water, carbon monoxide, nitrogen, and dicarbon molecules.