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

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

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

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

Journal Article · Wed Mar 30 00:00:00 EDT 2022 · Quantum

DOI:https://doi.org/10.22331/q-2022-03-30-675· OSTI ID:1860271

Keen, Trevor ^[1]; Peng, Bo ^[2]; Kowalski, Karol ^[2]; Lougovski, Pavel ^[3]; Johnston, Steven ^[4]

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

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 $O (N^{5})$ 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 $O (N^{6})$ computational resources per time step.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725; AC05-76RL01830; SC0014664

OSTI ID:: 1860271

Alternate ID(s):: OSTI ID: 1868066
OSTI ID: 1885243

Report Number(s):: PNNL-SA-161451; 675

Journal Information:: Quantum, Journal Name: Quantum Vol. 6; ISSN 2521-327X

Publisher:: Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenCopyright Statement

Country of Publication:: Austria

Language:: English

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

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