## A Faster, Better Approach to Describe Many-Body Systems

*This hybrid quantum-classical approach for coupled-cluster Green’s function theory maintains accuracy while cutting computational costs*

## The Science ** **

Green’s functions are a useful tool to describe many-body systems in quantum physics. The advancement of quantum computing has unlocked new ways to calculate Green’s functions. Researchers from Pacific Northwest National Laboratory, the University of Tennessee at Knoxville, and Oak Ridge National Laboratory developed a hybrid quantum-classical approach for calculating the time-domain of a Green’s function based on coupled-cluster (CC) methods. This approach eliminates the need to prepare ground state calculations and thus does not require prior information about the system. Researchers demonstrated the accuracy of this approach with the Anderson Impurity Model, which is commonly used in many-body approaches.

## The Impact

Unlike other quantum-based Green’s function approaches, the calculations developed in this study do not use a variational quantum eigensolver. Instead, this approach calculates the reference state using a simple product state. This cuts computational costs but does not affect the accuracy of the calculation. Additionally, this method is highly versatile and can be easily generalized to many models. This method is especially beneficial when little is known about the system, as prior information is not required.

## Summary

Quantum simulations require state preparation, time evolution, and measurement. Many state preparation methods require prior knowledge of the system’s eigenvalue spectrum. For classical algorithms, computation of the CC Green’s function becomes constrained by memory and storage requirements. The hybrid quantum-classical method reported here circumvents these requirements by applying unitary operators to a simple product state to calculate the reference state. Here, a single CC amplitude from classical CC methods provides the controlled approximation for the quantum calculation of the time-domain impurity Green’s function. Researchers demonstrated the accuracy of this approach for two- and three-level Anderson Impurity Models on a quantum simulator. This approach provided an order of magnitude improvement over classical CC Green’s function calculations of the same order.

## Contact

Bo Peng

Pacific Northwest National Laboratory

peng398@pnnl.gov

Karol Kowalski

Pacific Northwest National Laboratory

karol.kowalski@pnnl.gov

## Funding

This work was supported by the Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, the Division of Chemical Sciences, Geosciences, and Biosciences; the DOE, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research program; the Laboratory Directed Research and Development program at Pacific Northwest National Laboratory; and the DOE, Office of Science, Office of Advanced Scientific Computing Research Quantum Algorithm Teams and Quantum Computing Application Teams programs.

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Published: July 12, 2022*

Keen, T., Peng, B., Kowalski, K., Lougovski, P., Johnston, S. (2022).Hybrid quantum-classical approach for coupled-cluster Green’s function theory. *Quantum* (Vol. 6, p. 675). DOI: 10.22331/q-2022-03-30-675.