Hybrid quantum-classical approach for coupled-cluster Green's function theory

Trevor Keen; Bo Peng; Karol Kowalski; Pavel Lougovski; Steven Johnston

doi:10.22331/q-2022-03-30-675

Hybrid quantum-classical approach for coupled-cluster Green’s function theory

Trevor Keen¹, Bo Peng², Karol Kowalski², Pavel Lougovski³, and Steven Johnston^1,4

¹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States of America
²Physical Sciences and Computational Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States of America
³Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
⁴Institute for Advanced Materials and Manufacturing, University of Tennessee, Knoxville, Tennessee 37996, United States of America

Published:	2022-03-30, volume 6, page 675
Eprint:	arXiv:2104.06981v4
Doi:	https://doi.org/10.22331/q-2022-03-30-675
Citation:	Quantum 6, 675 (2022).

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Abstract

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of $T$ gates that grows as $ \mathcal{O} \left(N^5 \right)$ per time step to calculate the impurity Green's function in the time domain, where $N$ is the total number of energy levels in the AIM. Since the number of $T$ gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires $ \mathcal{O} \left(N^6 \right)$ computational resources per time step.

Featured image: An overview of the quantum-classical coupled-cluster algorithm for computing the Green's function at local site $p$ of a fermionic model. Boxes in blue (green) indicate tasks completed on classical (quantum) computer hardware. $\mathbf{W}_p$ is the set of unitaries obtained using the CCGF fermion-to-unitary mapping.

► BibTeX data

@article{Keen2022hybridquantum,
  doi = {10.22331/q-2022-03-30-675},
  url = {https://doi.org/10.22331/q-2022-03-30-675},
  title = {Hybrid quantum-classical approach for coupled-cluster {G}reen's function theory},
  author = {Keen, Trevor and Peng, Bo and Kowalski, Karol and Lougovski, Pavel and Johnston, Steven},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {675},
  month = mar,
  year = {2022}
}

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[2] Z. H. Sun, G. Hagen, and T. Papenbrock, "Coupled-cluster theory for strong entanglement in nuclei", Physical Review C 108 1, 014307 (2023).

[3] Shota Kanasugi, Shoichiro Tsutsui, Yuya O. Nakagawa, Kazunori Maruyama, Hirotaka Oshima, and Shintaro Sato, "Computation of Green's function by local variational quantum compilation", Physical Review Research 5 3, 033070 (2023).

[4] Diksha Dhawan, Dominika Zgid, and Mario Motta, "Quantum Algorithm for Imaginary-Time Green’s Functions", Journal of Chemical Theory and Computation acs.jctc.4c00241 (2024).

[5] Bo Peng, Nicholas P. Bauman, Sahil Gulania, and Karol Kowalski, "Coupled cluster Green's function-Past, Present, and Future", arXiv:2107.04968, (2021).

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