Selected Configuration Interaction in a Basis of Cluster State Tensor Products

Abstract

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 intra-cluster hopping terms, 2) less obviously clusterable cases of bond breaking in N2 and F2, 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, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.

References in corpus (40)

• The density-matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• A deterministic alternative to the full configuration interaction quantum Monte Carlo method
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
• Automated construction of molecular active spaces from atomic valence orbitals
• Fermionic neural-network states for ab-initio electronic structure
• Cheap and near exact CASSCF with large active spaces
• Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• CASSCF with Extremely Large Active Spaces using the Adaptive Sampling Configuration Interaction Method
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Excited states using semistochastic heat-bath configuration interaction
• Fast Semistochastic Heat-Bath Configuration Interaction
• Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
• Adaptive multiconfigurational wave functions
• Exactly-embedded multiconfigurational self-consistent field theory using density matrix embedding: the localized active space self-consistent field method
• Machine Learning Configuration Interaction
• Efficient heat-bath sampling in Fock space
• Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes
• Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
• Active space decomposition with multiple sites: Density matrix renormalization group algorithm
• The Variational Localized Active Space Self-Consistent Field Method
• Deterministic construction of nodal surfaces within quantum Monte Carlo: the case of FeS
• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Using CIPSI nodes in diffusion Monte Carlo
• Development of Monte Carlo configuration interaction: Natural orbitals and second-order perturbation theory
• A renormalized excitonic method in terms of block excitations. Application to spin lattices
• An efficient deterministic perturbation theory for selected configuration interaction methods
• Calculating excited states of molecular aggregates by the renormalized excitonic method
• Density-Matrix Renormalization Group Algorithm with Multi-Level Active Space
• DMRG Approach to Optimizing Two-Dimensional Tensor Networks
• Self-Adaptive Tensor Network States with Multi-Site Correlators
• Excitonic Coupled-cluster Theory

Cited by in corpus (16)

• Quantum Computing for Molecular Biology
• The Shape of Full Configuration Interaction to Come
• Matrix product states with large sites
• ADAPT-QSCI: Adaptive Construction of an Input State for Quantum-Selected Configuration Interaction
• Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• Construction of linearly independent non-orthogonal AGP states
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Cluster many-body expansion: a many-body expansion of the electron correlation energy about a cluster mean-field reference
• Symmetry-projected cluster mean-field theory applied to spin systems
• Quantum-selected configuration interaction with time-evolved state
• Linear combinations of cluster mean-field states applied to spin systems
• FragPT2: Multi-Fragment Wavefunction Embedding with Perturbative Interactions
• Efficient simulation of inhomogeneously correlated systems using block interaction product states
• Fault-tolerant Quantum Chemical Calculations with Improved Machine-Learning Models
• Coupled electron pair-type approximations for tensor product state wavefunctions