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

• URL: http://arxiv.org/abs/2310.10412v3
• Date: Thu, 03 Apr 2025 09:31:48 GMT
• Title: Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Authors: Gino Bishop, Dmitry Bagrets, Frank K. Wilhelm,
• Abstract summary: We propose a new quantum algorithm, which uses an analog the Kubo formula adapted to a quantum circuit the Hubbard model.<n>It allows to access the Green's cluster function directly using only bilinears of fermionic operators and circumvents the usage of the Hadamard test.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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