Generalized Unitary Coupled Cluster Wave functions for Quantum Computation

Lee, Joonho; Huggins, William J.; Head-Gordon, Martin; Whaley, K. Birgitta

doi:10.1021/acs.jctc.8b01004

Title: Generalized Unitary Coupled Cluster Wave functions for Quantum Computation

Journal Article · Wed Nov 28 00:00:00 EST 2018 · Journal of Chemical Theory and Computation

DOI:https://doi.org/10.1021/acs.jctc.8b01004· OSTI ID:1605226

^[1]; Huggins, William J. ^[1];

^[1]; Whaley, K. Birgitta ^[1]

Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

We introduce a unitary coupled-cluster (UCC) ansatz termed k-UpCCGSD that is based on a family of sparse generalized doubles operators, which provides an affordable and systematically improvable unitary coupled-cluster wave function suitable for implementation on a near-term quantum computer. k-UpCCGSD employs k products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized single and double excitation operators (UCCGSD), as well as with the standard ansatz employing only single and double excitations (UCCSD). k-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of ^O(kN), compared with ^O(N³) for UCCGSD, and ^{O((N-η)²η)} for UCCSD, where N is the number of spin orbitals and η is the number of electrons. We analyzed the accuracy of these three ansätze by making classical benchmark calculations on the ground state and the first excited state of H₄ (STO-3G, 6-31G), H₂O (STO-3G), and N₂ (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that k-UpCCGSD offers a good trade-off between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. UCCGSD is also found to be more accurate than UCCSD but at a greater cost for implementation. Excited states are calculated with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. Lastly, we demonstrate that using a specialized multideterminantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1605226

Journal Information:: Journal of Chemical Theory and Computation, Vol. 15, Issue 1; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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