The Full Configuration Interaction Quantum Monte Carlo Method through the Lens of Inexact Power Iteration

Lu, Jianfeng; Wang, Zhe

doi:10.1137/18m1166626

Cited by 13 publications

(17 citation statements)

References 34 publications

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“…This method has been discussed previously and compared to FCIQMC. 25 As discussed above, its memory and CPU cost TABLE I. An overview of the steps in each iteration of the FCI-FRI methods considered in this study.…”

Section: Fci-fri Methods Considered In This Studymentioning

confidence: 99%

“…An additional purpose of this work is to better understand how the features of each of these methods influence their errors and computational cost. To this end, we also compare two methods applied recently to FCI problems 25 in which the matrix is not compressed. Although expensive, such approaches are feasible because of the sparse structure of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration

Greene

Webber

Weare

et al. 2019

J. Chem. Theory Comput.

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We introduce a family of methods for the full configuration interaction problem in quantum chemistry, based on the fast randomized iteration (FRI) framework [L.-H. Lim and J. Weare, SIAM Rev. 59, 547 (2017)]. 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 to 45 times more statistically efficient than the multinomial FCI-FRI scheme, which is in turn 1.4 to 178 times more statistically efficient than the original FCIQMC algorithm.

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Section: Fci-fri Methods Considered In This Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration

Greene

Webber

Weare

et al. 2019

J. Chem. Theory Comput.

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“…In recent years a new family of projector MC methods, first and foremost among these FCIQMC, has emerged where the Fermion sign problem is circumvented without recourse to the FNA . Similarly to DMC, these are still projector methods, but the stochastic propagation is not formulated in real space, but rather in Fock space. For a suitably small time‐step, δτ , the Green's function for the imaginary‐time Schrödinger equation can be approximated by its linear term.…”

Section: Reduced‐scaling: Alternative Approachesmentioning

confidence: 99%

Reduced‐scaling coupled cluster response theory: Challenges and opportunities

Crawford

Kumar

Bazanté

et al. 2019

WIREs Comput Mol Sci

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We review the current state of reduced-scaling electron correlation methods, particularly coupled-cluster theory for the simulation and prediction of molecular response properties. The successes of local-coupled-cluster and related approaches are well known for reaction energies, thermodynamic constants, dipole moments, and so forth-properties that depend primarily on the quality of the ground-state wave function. However, much more challenging are higher-order properties such as polarizabilities, hyperpolarizabilities, optical rotations, magnetizabilities, and others that also require accurate representation of the derivative of the wave function to external electromagnetic fields. We discuss a range of methods for improving the correlation domains of such perturbed wave functions, including the use of "perturbation-aware" natural orbitals that are customized for the property of interest. In addition, we consider the viability and potential of promising, but stillemerging methods such as stochastic and real-time coupled-cluster approaches, for which the localizability of the field-dependent wave function may be more controllable than for conventional response theory.

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“…In quantum chemistry and physics literature, several selected configuration interaction (CI) method have been developed to solve (1.2) by selecting important Slater determinant basis [12,34,36]. These methods have been shown be competitive or sometimes better than Monte-Carlo based methods for sampling rows and columns of A stochastically [6,7,19].…”

Section: Introductionmentioning

confidence: 99%

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

Zhou¹

2021

CSIAM-AM

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We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. This type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing the eigenvalue of a k×k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

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The Full Configuration Interaction Quantum Monte Carlo Method through the Lens of Inexact Power Iteration

Cited by 13 publications

References 34 publications

Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration

Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration

Reduced‐scaling coupled cluster response theory: Challenges and opportunities

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

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