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.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.

arXiv:2002.03107Journal of Chemical Theory and ComputationAug 26, 202065 citations

Configuration Interaction Monte Carlo with Coupled Clusters Wave Functions

Alessandro Roggero, Paolo Mori, Abhishek Mukherjee +1 more

Advances in quantum chemistryJan 1, 20161 citation

Coupled cluster analysis of model non-adiabetic Hamiltonians

D. J. van der Walt, Joseph P. Michael

Apr 25, 20070 citations

Perturbatively expanded sample-based quantum diagonalization for ground state energy calculation

M. Bovoloni, A. Famulari, P. Macchi

The Selected Quantum Doubles (SQD) methods are among the most reliable approaches for quantum computation, capable of achieving high-accuracy simulations of electronic structure problems. Despite their strengths, SQD methods encounter challenges related to the selection of the initial state and the efficient management of extensive configuration spaces. This is particularly due to the presence of numerous configurations with low significance, which can limit scalability and accuracy. To address these issues, we have developed a perturbative quantum method capable of generating an initial state that is both accurate and flexible, alongside a procedure to manage the scalability of the method. Regarding the first objective, a parameterized Unitary Coupled Cluster Doubles (UCCD) approach has been developed, which generates a wavefunction comparable in quality to the Coupled Cluster Doubles (CCD) reference state. At this juncture, it is possible to augment this parameterized UCCD state to incorporate the principal single excited configurations. This augmentation step is essential to ensure that the initial state possesses sufficient flexibility to account for configurations that are combinations of single and double excited configurations. The second objective is the enhancement of the methodology's scalability. This objective is achieved by first identifying, through a perturbative approach, the most significant higher-order configurations. This allows for a smaller configurational CI Hamiltonian. Conversely, the second set of configurations will not be included in the Hamiltonian CI but will be evaluated solely within a perturbative framework using second-order perturbation theory (PT2). This combined approach leverages the strengths of both variational and perturbative methods, enabling the simulation to closely approximate Full Configuration Interaction (FCI) results while operating within a significantly reduced configurational space. This methodology resembles the most common Selected Configurations Interaction plus Perturbation methodology, while distinguishing itself through an improved selection process, which will be further refined in the future. The method will be tested on a highly correlated molecular system (linear chain of 8 Hydrogen) in minimal basis set. The molecule has been optimized in pyscf with MP2 method and def2-svp basis set.The Selected Quantum Doubles (SQD) methods are among the most reliable approaches for quantum computation, capable of achieving high-accuracy simulations of electronic structure problems. Despite their strengths, SQD methods encounter challenges related to the selection of the initial state and the efficient management of extensive configuration spaces. This is particularly due to the presence of numerous configurations with low significance, which can limit scalability and accuracy. To address these issues, we have developed a perturbative quantum method capable of generating an initial state that is both accurate and flexible, alongside a procedure to manage the scalability of the method. Regarding the first objective, a parameterized Unitary Coupled Cluster Doubles (UCCD) approach has been developed, which generates a wavefunction comparable in quality to the Coupled Cluster Doubles (CCD) reference state. At this juncture, it is possible to augment this parameterized UCCD state to incorporate the principal single excited configurations. This augmentation step is essential to ensure that the initial state possesses sufficient flexibility to account for configurations that are combinations of single and double excited configurations. The second objective is the enhancement of the methodology's scalability. This objective is achieved by first identifying, through a perturbative approach, the most significant higher-order configurations. This allows for a smaller configurational CI Hamiltonian. Conversely, the second set of configurations will not be included in the Hamiltonian CI but will be evaluated solely within a perturbative framework using second-order perturbation theory (PT2). This combined approach leverages the strengths of both variational and perturbative methods, enabling the simulation to closely approximate Full Configuration Interaction (FCI) results while operating within a significantly reduced configurational space. This methodology resembles the most common Selected Configurations Interaction plus Perturbation methodology, while distinguishing itself through an improved selection process, which will be further refined in the future. The method will be tested on a highly correlated molecular system (linear chain of 8 Hydrogen) in minimal basis set. The molecule has been optimized in pyscf with MP2 method and def2-svp basis set.

Jan 1, 20260 citations

Symmetry projection methods in strongly correlated systems

Ruiheng Song

Quantum chemistry aims to understand and predict molecular structure and properties by solving the time-independent Schr\"odinger equation within fixed nuclei (Born-Oppenheimer) approximation. The Hamiltonian may have continuous symmetries (e.g., spin) or discrete symmetries (for example, point group). Mean-field wave functions may break some or all of these symmetries. By taking the symmetry-adapted pieces of these broken symmetry states, one can restore the physical character of the wave function while also treating relevant strong correlations. On the other hand, mean-field methods lack dynamic correlation arising from short-range interactions. Still, single-reference methods such as configuration interaction or coupled cluster theory can handle these correlations efficiently. Ideally, we would like to combine these approaches: performing configuration interaction or coupled cluster theory on a broken symmetry reference while restoring the desired symmetries. This work introduces a new approach to integrating symmetry projection and coupled cluster theory. By borrowing techniques from previous research, the new method can restore continuous symmetries like $U$ (1) and $SU$ (2) and discrete symmetries like point group and time reversal. This method achieves accurate results in challenging systems and has the same computational scaling as traditional coupled cluster theory. Jordan-Wigner transformation is a potent tool in spin models, but its application is challenging due to the inherent strings. The same techniques we use to combine symmetry projection and coupled cluster theory can be used to combine Jordan-Wigner transformation and coupled cluster. The strings are the ' symmetry projection ' operator when constructing the Hartree-Fock and coupled cluster wave functions for a Jordan-Wigner transformed Hamiltonian. Leveraging the method of symmetry projection, we obtain excellent results for both 1-D and 2-D spin models.Quantum chemistry aims to understand and predict molecular structure and properties by solving the time-independent Schr\"odinger equation within fixed nuclei (Born-Oppenheimer) approximation. The Hamiltonian may have continuous symmetries (e.g., spin) or discrete symmetries (for example, point group). Mean-field wave functions may break some or all of these symmetries. By taking the symmetry-adapted pieces of these broken symmetry states, one can restore the physical character of the wave function while also treating relevant strong correlations. On the other hand, mean-field methods lack dynamic correlation arising from short-range interactions. Still, single-reference methods such as configuration interaction or coupled cluster theory can handle these correlations efficiently. Ideally, we would like to combine these approaches: performing configuration interaction or coupled cluster theory on a broken symmetry reference while restoring the desired symmetries. This work introduces a new approach to integrating symmetry projection and coupled cluster theory. By borrowing techniques from previous research, the new method can restore continuous symmetries like $U$(1) and $SU$(2) and discrete symmetries like point group and time reversal. This method achieves accurate results in challenging systems and has the same computational scaling as traditional coupled cluster theory. Jordan-Wigner transformation is a potent tool in spin models, but its application is challenging due to the inherent strings. The same techniques we use to combine symmetry projection and coupled cluster theory can be used to combine Jordan-Wigner transformation and coupled cluster. The strings are the ' symmetry projection ' operator when constructing the Hartree-Fock and coupled cluster wave functions for a Jordan-Wigner transformed Hamiltonian. Leveraging the method of symmetry projection, we obtain excellent results for both 1-D and 2-D spin models.

Sep 30, 20240 citations

INTERMEDIATE HAMILTONIAN FOCK-SPACE COUPLED CLUSTER METHOD AND APPLICATIONS

Arie Landau, Ephraim Eliav, Uzi Kaldor

Recent Progress in Many-Body TheoriesDec 1, 20021 citation

U

(1) and

SU

(2) and discrete symmetries like point group and time reversal. This method achieves accurate results in challenging systems and has the same computational scaling as traditional coupled cluster theory. Jordan-Wigner transformation is a potent tool in spin models, but its application is challenging due to the inherent strings. The same techniques we use to combine symmetry projection and coupled cluster theory can be used to combine Jordan-Wigner transformation and coupled cluster. The strings are the ' symmetry projection ' operator when constructing the Hartree-Fock and coupled cluster wave functions for a Jordan-Wigner transformed Hamiltonian. Leveraging the method of symmetry projection, we obtain excellent results for both 1-D and 2-D spin models.