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arXiv · 2310.10412

Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model

Gino Bishop·Dmitry Bagrets·Frank K. Wilhelm
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Abstract

In the framework of the hybrid quantum-classical variational cluster approach (VCA) to strongly correlated electron systems one of the goals of a quantum subroutine is to find single-particle correlation functions of lattice fermions in polynomial time. Previous works suggested to use variants of the Hadamard test for this purpose, which requires an implementation of controlled single-particle fermionic operators. However, for a number of locality-preserving mappings to encode fermions into qubits, a direct construction of such operators is not possible. In this work, we propose a new quantum algorithm, which uses an analog of the Kubo formula adapted to a quantum circuit simulating the Hubbard model. It allows to access the Green's function of a cluster directly using only bilinears of fermionic operators and circumvents the usage of the Hadamard test. We test our new algorithm in practice by using open-access simulators of noisy IBM superconducting chips.

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Gino Bishop, Dmitry Bagrets, Frank K. Wilhelm. 2025-04-03. Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model. https://doi.org/10.1103/physreva.111.062610

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