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

Trevor Keen1, Bo Peng2, Karol Kowalski2, Pavel Lougovski3, and Steven Johnston1,4

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

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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.

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Cited by

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

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