Physical and mathematical content of coupled-cluster equations. IV. Impact of approximations to the cluster operator on the structure of solutions

1999 ◽  
Vol 111 (7) ◽  
pp. 2952-2959 ◽  
Author(s):  
K. Jankowski ◽  
K. Kowalski
Keyword(s):  
Coupled Cluster ◽  
Structure Of Solutions ◽  
Mathematical Content ◽  
Cluster Operator

scholarly journals Low rank representations for quantum simulation of electronic structure

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Mario Motta ◽  
Erika Ye ◽  
Jarrod R. McClean ◽  
Zhendong Li ◽  
Austin J. Minnich ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Nearest Neighbor ◽  
Quantum Simulation ◽  
Low Rank ◽  
Coupled Cluster ◽  
Iron Sulfur Clusters ◽  
Cluster Operator ◽  
Basis Size ◽  
Promising Application ◽  
Rank Factorization

AbstractThe quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $${\mathcal{O}}({N}^{4})$$ O ( N 4 ) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity in small simulations, which reduces to $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) depth on a linearly connected array, an improvement over the $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 105 non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.

scholarly journals Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1101 ◽  
Author(s):  
Alexander V. Oleynichenko ◽  
Andréi Zaitsevskii ◽  
Leonid V. Skripnikov ◽  
Ephraim Eliav
Keyword(s):  
Electronic Structure ◽  
Fock Space ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Heavy Nuclei ◽  
Coupled Cluster Method ◽  
Molecular Systems ◽  
Cluster Operator ◽  
Zero Shift ◽  
Firm Basis

The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.

The relativistic coupled-cluster method: transition energies of bismuth and eka-bismuth

1998 ◽  
Vol 94 (1) ◽  
pp. 181-187 ◽  
Author(s):  
EPHRAIM ELIAV ◽  
UZI KALDOR ◽  
YASUYUKI ISHIKAWA
Keyword(s):  
Cluster Method ◽  
Coupled Cluster ◽  
Coupled Cluster Method ◽  
Transition Energies

Adiabatic electron affinities of PF5 and SF6: a coupled-cluster study

1998 ◽  
Vol 94 (1) ◽  
pp. 121-125 ◽  
Author(s):  
Gennady GUTSEV ◽  
RODNEY BARTLETT
Keyword(s):  
Coupled Cluster ◽  
Electron Affinities
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