On the difference between variational and unitary coupled cluster theories

Harsha, Gaurav; Shiozaki, Toru; Scuseria, Gustavo E.

doi:10.1063/1.5011033

Title: On the difference between variational and unitary coupled cluster theories

Journal Article · Sun Jan 28 00:00:00 EST 2018 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5011033· OSTI ID:1512944

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Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
Northwestern Univ., Evanston, IL (United States). Dept. of Chemistry
Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy, and Dept. of Chemistry

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

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Research Organization:: Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0001474; FG02-09ER16053

OSTI ID:: 1512944

Alternate ID(s):: OSTI ID: 1417782

Journal Information:: Journal of Chemical Physics, Vol. 148, Issue 4; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 57 works

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An adaptive variational algorithm for exact molecular simulations on a quantum computer Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-10988-2	journal	July 2019
Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications Liu, Junzi; Asthana, Ayush; Cheng, Lan The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5030344	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 Bauman, Nicholas P.; Bylaska, Eric J.; Krishnamoorthy, Sriram The Journal of Chemical Physics, Vol. 151, Issue 1 https://doi.org/10.1063/1.5094643	journal	July 2019
Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer Yen, Tzu-Ching; Lang, Robert A.; Izmaylov, Artur F. The Journal of Chemical Physics, Vol. 151, Issue 16 https://doi.org/10.1063/1.5110682	journal	October 2019
Exact parameterization of fermionic wave functions via unitary coupled cluster theory Evangelista, Francesco A.; Chan, Garnet Kin-Lic; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 151, Issue 24 https://doi.org/10.1063/1.5133059	journal	December 2019
Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions Barkoutsos, Panagiotis Kl.; Gonthier, Jerome F.; Sokolov, Igor Physical Review A, Vol. 98, Issue 2 https://doi.org/10.1103/physreva.98.022322	journal	August 2018
Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions Barkoutsos, Panagiotis Kl.; Gonthier, Jerome F.; Sokolov, Igor arXiv https://doi.org/10.48550/arxiv.1805.04340	text	January 2018
An adaptive variational algorithm for exact molecular simulations on a quantum computer Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin arXiv https://doi.org/10.48550/arxiv.1812.11173	text	January 2018
Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory Evangelista, Francesco A.; Chan, Garnet Kin-Lic; Scuseria, Gustavo E. arXiv https://doi.org/10.48550/arxiv.1910.10130	text	January 2019
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