Beyond MP2 initialization for unitary coupled cluster quantum circuits

Mark R. Hirsbrunner; Diana Chamaki; J. Wayne Mullinax; Norm M. Tubman

doi:10.22331/q-2024-11-26-1538

Beyond MP2 initialization for unitary coupled cluster quantum circuits

Mark R. Hirsbrunner^1,2, Diana Chamaki², J. Wayne Mullinax^3,4, and Norm M. Tubman⁴

¹Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
²USRA Research Institute for Advanced Computer Science, Mountain View, California 94043, USA
³KBR, Inc., NASA Ames Research Center, Moffett Field, California 94035, USA
⁴Intelligent Systems Division, NASA Ames Research Center, Moffett Field, California 94035, USA

Published:	2024-11-26, volume 8, page 1538
Eprint:	arXiv:2301.05666v4
Doi:	https://doi.org/10.22331/q-2024-11-26-1538
Citation:	Quantum 8, 1538 (2024).

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Abstract

The unitary coupled cluster (UCC) ansatz is a promising tool for achieving high-precision results using the variational quantum eigensolver (VQE) algorithm in the NISQ era. However, results on quantum hardware are thus far very limited and simulations have only accessed small system sizes. We advance the state of the art of UCC simulations by utilizing an efficient sparse wavefunction circuit solver and studying systems up to 64 qubits. Here we report results obtained using this solver that demonstrate the power of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction, among others. Our approach enables meaningful benchmarking of the UCC ansatz, a crucial step in assessing the utility of VQE for achieving quantum advantage.

Featured image: This figure depicts the convergence of the correlation energy of the molecule $\mathrm{CH}_2\mathrm{O}$ calculated using the unitary coupled cluster (UCC) ansatz as a function of the number of determinants utilized by the sparse wavefunction simulator, $N_{\text{WF}}$. The dot-dashed lines indicate the energy obtained by the classical simulation method coupled cluster singles and doubles (CCSD), and the dotted line gives the energy provided by CCSD with perturbative triples, the best available reference energy. The solid and dashed lines in (a) correspond to parameterizing the UCC ansatz using Møller–Plesset perturbation theory of the second order (MP2) and CCSD, respectively. Panel (b) shows quadratic fits of these energies as a function of $1/N_{\text{WF}}$, extrapolating to the exact limit $N_{\text{WF}}\rightarrow\infty$.

► BibTeX data

@article{Hirsbrunner2024beyondmp,
  doi = {10.22331/q-2024-11-26-1538},
  url = {https://doi.org/10.22331/q-2024-11-26-1538},
  title = {Beyond {MP}2 initialization for unitary coupled cluster quantum circuits},
  author = {Hirsbrunner, Mark R. and Chamaki, Diana and Mullinax, J. Wayne and Tubman, Norm M.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1538},
  month = nov,
  year = {2024}
}

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