Exact parameterization of fermionic wave functions via unitary coupled cluster theory

Evangelista, Francesco A.; Chan, Garnet Kin-Lic; Scuseria, Gustavo E.

doi:10.1063/1.5133059

Title: Exact parameterization of fermionic wave functions via unitary coupled cluster theory

Journal Article · 25 December 2019 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5133059 · OSTI ID:1602045

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Emory Univ., Atlanta, GA (United States); Emory University
California Institute of Technology (CalTech), Pasadena, CA (United States)
Rice Univ., Houston, TX (United States)

In this study, a formal analysis is conducted on the exactness of various forms of unitary coupled cluster (UCC) theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a factorized (referred to here as “disentangled”) version are considered. We formulate a differential cluster analysis to determine the UCC amplitudes corresponding to a general quantum state. The exactness of conventional UCC (ability to represent any state) is explored numerically, and it is formally shown to be determined by the structure of the critical points of the UCC exponential mapping. A family of disentangled UCC wave functions is proven to exactly parameterize any state, thus showing how to construct Trotter-error-free parameterizations of UCC for applications in quantum computing. In conclusion, from these results, we construct an exact disentangled UCC parameterization that employs an infinite sequence of particle-hole or general one- and two-body substitution operators.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States); Emory Univ., Atlanta, GA (United States); Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division

Grant/Contract Number:: SC0019374

OSTI ID:: 1602045

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 24 Vol. 151; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

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