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On the difference between variational and unitary coupled cluster theories

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.5011033· OSTI ID:1512944
 [1];  [2];  [3]
  1. Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy; none
  2. Northwestern Univ., Evanston, IL (United States). Dept. of Chemistry
  3. Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy, and Dept. of Chemistry
+ Show Author Affiliations
There have been assertions in the literature that the variational and unitary forms of coupled cluster theory lead to the same energy functional. Numerical evidence from previous authors was inconsistent with this claim, yet the small energy differences found between the two methods and the relatively large number of variational parameters precluded an unequivocal conclusion. Using the Lipkin Hamiltonian, we here present conclusive numerical evidence that the two theories yield different energies. The ambiguities arising from the size of the cluster parameter space are absent in the Lipkin model, particularly when truncating to double excitations. We show that in the symmetry adapted basis under strong correlation, the differences between the variational and unitary models are large, whereas they yield quite similar energies in the weakly correlated regime previously explored. We also provide a qualitative argument rationalizing why these two models cannot be the same. Additionally, we study a generalized non-unitary and non-hermitian variant that contains excitation, de-excitation, and mixed operators with different amplitudes and show that it works best when compared to the traditional, variational, unitary, and extended forms of coupled cluster doubles theories
Research Organization:
Rice Univ., Houston, TX (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
SC0001474
OSTI ID:
1512944
Alternate ID(s):
OSTI ID: 1417782
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 148; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (11)

An adaptive variational algorithm for exact molecular simulations on a quantum computer journal July 2019
Simulating Many-Body Systems with a Projective Quantum Eigensolver text January 2021
Variational Quantum Simulation for Quantum Chemistry journal January 2019
Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications journal June 2018
Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms journal July 2019
Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer journal October 2019
Exact parameterization of fermionic wave functions via unitary coupled cluster theory journal December 2019
Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions journal August 2018
Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions text January 2018
An adaptive variational algorithm for exact molecular simulations on a quantum computer text January 2018
Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory text January 2019

Figures / Tables (4)

FIG. 1(p. 3)figure FIG. 1
FIG. 2(p. 5)figure FIG. 2
FIG. 3(p. 5)figure FIG. 3
FIG. 4(p. 5)figure FIG. 4

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