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Ground-State Preparation of the Fermi-Hubbard Model on a Quantum Computer with 2D Topology via Quantum Eigenvalue Transformation of Unitary Matrices
Thilo R. Müller, Manuel Geiger, Christian B. Mendl
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Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of quantum systems. The Fermi-Hubbard model, particularly, is of profound interest due to its implications for high-temperature superconductivity and strongly correlated electron systems. The quantum eigenvalue transformation of unitary matrices (QETU) algorithm offers a novel approach for ground state estimation by utilizing a controlled Hamiltonian time evolution operator, circumventing the resource-intensive block-encoding required by previous methods. In this work, we apply the QETU algorithm to the 2 ×2 Fermi-Hubbard model, presenting circuit simplifications tailored to the model and introducing a mapping to a 9-qubit grid-like hardware architecture inspired by fermionic swap networks. We investigate how the selection of a favorable hardware architecture can benefit the circuit construction. Additionally, we explore the feasibility of this method under the influence of noise, focusing on its robustness and practical applicability.
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