Adam A. Holmes

Bio: Adam A. Holmes is an academic researcher from Cornell University. The author has contributed to research in topics: Configuration interaction & Slater determinant. The author has an hindex of 11, co-authored 13 publications receiving 1261 citations. Previous affiliations of Adam A. Holmes include University of Colorado Boulder.

Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling

Abstract: We introduce a new selected configuration interaction plus perturbation theory algorithm that is based on a deterministic analog of our recent efficient heat-bath sampling algorithm. This Heat-bath Configuration Interaction (HCI) algorithm makes use of two parameters that control the trade-off between speed and accuracy, one which controls the selection of determinants to add to a variational wave function and one which controls the selection of determinants used to compute the perturbative correction to the variational energy. We show that HCI provides an accurate treatment of both static and dynamic correlation by computing the potential energy curve of the multireference carbon dimer in the cc-pVDZ basis. We then demonstrate the speed and accuracy of HCI by recovering the full configuration interaction energy of both the carbon dimer in the cc-pVTZ basis and the strongly correlated chromium dimer in the Ahlrichs VDZ basis, correlating all electrons, to an accuracy of better than 1 mHa, in just a few mi...

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory

Abstract: We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 2016, 12, 3674], by introducing a semistochastic algorithm for performing multireference Epstein–Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis–Hastings sampling, we use the Alias method to directly sample determinants from the reference wave function, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI) is faster than the deterministic variant for many systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly para...

Semistochastic Projector Monte Carlo Method

Abstract: We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectationvalues only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer. Introduction.—Consider the computation of the domi- nant eigenvalue of an NN matrix, with N so large that the matrix cannot be stored. Transformation methods can- not be used in this case, but one can still proceed with the power method, also known as the projection method, as long as one can compute and store the result of multi- plication of an arbitrary vector by the matrix. When, for sufficiently large N, this is no longer feasible, Monte Carlo methods can be used to represent stochastically both the vector and multiplication by the matrix. This suffices to implement the power method to compute the dominant eigenvalue and averages involving its corresponding eigenvector. In this Letter, we propose a hybrid method consisting of numerically exact representation and multiplication in a small deterministic subspace, complemented by stochastic treatment of the rest of the space. This semistochastic projection method combines the advantages of both approaches: it greatly reduces the statistical uncertainty of averages relative to purely stochastic projection while allowing N to be large. These advantages are realized if one succeeds in choosing a deterministic subspace that carries a substantial fraction of the total spectral weight of the dominant eigenstate. Semistochastic projection has numerous potential applications: transfer matrix (1) and quantum Monte Carlo (QMC) (2-4) calculations, respectively for classical statistical mechanical and quantum mechanical systems, and the calculation of subdominant eigenvalues (5).

Cheap and Near Exact CASSCF with Large Active Spaces

Abstract: We use the recently developed Heat-bath Configuration Interaction (HCI) algorithm as an efficient active space solver to perform multiconfiguration self-consistent field calculations (HCISCF) with large active spaces. We give a detailed derivation of the theory and show that difficulties associated with non-variationality of the HCI procedure can be overcome by making use of the Lagrangian formulation to calculate the HCI relaxed two-body reduced density matrix. HCISCF is then used to study the electronic structure of butadiene, pentacene, and Fe–porphyrin. One of the most striking results of our work is that the converged active space orbitals obtained from HCISCF are relatively insensitive to the accuracy of the HCI calculation. This allows us to obtain nearly converged CASSCF energies with an estimated error of less than 1 mHa using the orbitals obtained from the HCISCF procedure in which the integral transformation is the dominant cost. For example, an HCISCF calculation on the Fe–porphyrin model comp...

Excited states using semistochastic heat-bath configuration interaction.

Abstract: We extend our recently developed heat-bath configuration interaction (HCI) algorithm, and our semistochastic algorithm for performing multireference perturbation theory, to calculate excited-state wavefunctions and energies. We employ time-reversal symmetry, which reduces the memory requirements by more than a factor of two. An extrapolation technique is introduced to reliably extrapolate HCI energies to the full CI limit. The resulting algorithm is used to compute fourteen low-lying potential energy surfaces of the carbon dimer using the cc-pV5Z basis set, with an estimated error in energy of 30-50 μHa compared to full CI. The excitation energies obtained using our algorithm have a mean absolute deviation of 0.02 eV compared to experimental values.

An adaptive variational algorithm for exact molecular simulations on a quantum computer.

Abstract: Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.

Recent developments in the PySCF program package

Abstract: PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

Abstract: This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling

Abstract: We introduce a new selected configuration interaction plus perturbation theory algorithm that is based on a deterministic analog of our recent efficient heat-bath sampling algorithm. This Heat-bath Configuration Interaction (HCI) algorithm makes use of two parameters that control the trade-off between speed and accuracy, one which controls the selection of determinants to add to a variational wave function and one which controls the selection of determinants used to compute the perturbative correction to the variational energy. We show that HCI provides an accurate treatment of both static and dynamic correlation by computing the potential energy curve of the multireference carbon dimer in the cc-pVDZ basis. We then demonstrate the speed and accuracy of HCI by recovering the full configuration interaction energy of both the carbon dimer in the cc-pVTZ basis and the strongly correlated chromium dimer in the Ahlrichs VDZ basis, correlating all electrons, to an accuracy of better than 1 mHa, in just a few mi...

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory

Abstract: We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 2016, 12, 3674], by introducing a semistochastic algorithm for performing multireference Epstein–Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis–Hastings sampling, we use the Alias method to directly sample determinants from the reference wave function, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI) is faster than the deterministic variant for many systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly para...