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arXiv:2603.16605

Quantum Algorithms to Determine Spin-Resolved Exchange-Correlation Potential for Strongly Correlated Materials

H. Arslan Hashim, Volodymyr Turkowski, Eduardo R. Mucciolo

Published Mar 17, 2026• 0 citations
arXivHTMLPDF

Abstract

Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine spin-resolved XC potentials using a variational quantum eigensolver. Using the Hubbard model as a prototypical strongly correlated lattice system, we prepare ground states in fixed spin sectors through a Hamiltonian variational ansatz initialized from the non-interacting $(U=0)$ Slater-determinant ground state. From the resulting many-body ground states, we extract the XC energy and compute the corresponding spin-resolved XC potentials via finite differences. The accuracy of the approach is benchmarked against exact diagonalization for one- and two-dimensional Hubbard systems of various lattice sizes. We demonstrate that the variational ansatz reproduces the ground-state energies and densities with high fidelity, enabling accurate construction of both magnetic and non-magnetic XC potentials. We analyzed the dependence of the XC potentials on the interaction strength, charge, spin densities, and magnetization. We also present an empirical complexity scaling relation for the computational cost of the method at a fixed fidelity. These results illustrate how quantum computing can be used to construct spin-resolved XC functionals for correlated lattice models, providing a potential pathway for improving density functional approximations in strongly correlated materials.

DOI
10.48550/arxiv.2603.16605

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Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine spin-resolved XC potentials using a variational quantum eigensolver. Using the Hubbard model as a prototypical strongly correlated lattice system, we prepare ground states in fixed spin sectors through a Hamiltonian variational ansatz initialized from the non-interacting (U=0)(U=0)(U=0) Slater-determinant ground state. From the resulting many-body ground states, we extract the XC energy and compute the corresponding spin-resolved XC potentials via finite differences. The accuracy of the approach is benchmarked against exact diagonalization for one- and two-dimensional Hubbard systems of various lattice sizes. We demonstrate that the variational ansatz reproduces the ground-state energies and densities with high fidelity, enabling accurate construction of both magnetic and non-magnetic XC potentials. We analyzed the dependence of the XC potentials on the interaction strength, charge, spin densities, and magnetization. We also present an empirical complexity scaling relation for the computational cost of the method at a fixed fidelity. These results illustrate how quantum computing can be used to construct spin-resolved XC functionals for correlated lattice models, providing a potential pathway for improving density functional approximations in strongly correlated materials.
Abstract The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems. In this study, the ground, first, and second excited state energies of 4$\times1and21 and 21and2\times$2 Hubbard lattices are obtained using a newly designed ansatz circuit. The ansatz is constructed by combining concepts from the Hamiltonian Variational Ansatz (HVA) and the Number-Preserving Ansatz (NPA). A hybrid optimization strategy is applied, where COBYLA is used for coarse convergence and L-BFGS for fine-tuning. The resulting energies are evaluated, and the corresponding physical properties of the systems are analyzed through phase diagrams of the energy excitation gaps for different charge and spin configurations.
The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems. In this study, the ground, first, and second excited state energies of 4$\times1and21 and 21and2\times$2 Hubbard lattices are obtained using a newly designed ansatz circuit. The ansatz is constructed by combining concepts from the Hamiltonian Variational Ansatz (HVA) and the Number-Preserving Ansatz (NPA). A hybrid optimization strategy is applied, where COBYLA is used for coarse convergence and L-BFGS for fine-tuning. The resulting energies are evaluated, and the corresponding physical properties of the systems are analyzed through phase diagrams of the energy excitation gaps for different charge and spin configurations.
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The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate Ca2CuO3{\mathrm{Ca}}_{2}{\mathrm{Cu}\mathrm{O}}_{3}Ca2​CuO3​, the excitonic ground state of monolayer WTe2{\mathrm{W}\mathrm{Te}}_{2}WTe2​, and the charge-ordered state of correlated metal SrVO3{\mathrm{Sr}\mathrm{VO}}_{3}SrVO3​. Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.
We illustrate the scope of time-dependent density-functional theory for strongly correlated (lattice) models out of equilibrium. Using the exact many-body time evolution, we reverse engineer the exact exchange correlation (xc) potential v_(xc) for small Hubbard chains exposed to time-dependent fields. We introduce an adiabatic local density approximation to v_(xc) for the 1D Hubbard model and compare it to exact results, to gain insight about approximate xc potentials. Finally, we provide some remarks on the v-representability for the 1D Hubbard model.
Abstract The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems, and is crucial for the understanding of notable quantum phenomena including superconductivity and magnetism. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high computational cost and is restricted to small samples, especially in two or higher dimensions. Here, we introduce a variational method in the frame of fermionic Gaussian states, and obtain the ground states of one- and two-dimensional attractive Hubbard models via imaginary-time evolution. We calculate the total energy and benchmark the results in a wide range of interaction strength and filling factor with those obtained via exact two-body results, the density matrix renormalization group based on matrix product states (MPS), and projector Quantum Monte Carlo (QMC) method. For both 1D and 2D cases, the Gaussian variational method presents accurate results for total energy with a maximum systematic error ∼ 4 % in the intermediate interaction region. The accuracy of these results has negligible dependence on the system size. We further calculate the double occupancy and find excellent agreement with MPS and QMC, as well as the experimental results of cold quantum gases in optical lattices. The results suggest that the Gaussian pairing state is a good approximation to the ground states of attractive Hubbard model, in particular in the strong and weak coupling limits. Moreover, we generalize the method to the attractive Hubbard model with a finite spin-polarization, which can be mapped to the repulsive interaction case via particle-hole transformation, and obtain accurate results of ground state energy and double occupancy. Our work demonstrates the ability of the Gaussian variational method to extract ground state properties of strongly correlated many-body systems with negligible computational cost, especially of large size and in higher dimensions.