Classical Benchmarks of a Symmetry-Adapted Variational Quantum Eigensolver for Real-Time Green's Functions in Dynamical Mean-Field Theory

TL;DR

This paper develops a symmetry-adapted variational quantum eigensolver for the Anderson Impurity Model within DMFT, demonstrating accurate ground state energies and Green's functions for larger baths, especially in strong interactions, on near-term quantum hardware.

Contribution

It introduces a symmetry-preserving VQE approach for larger bath discretizations in DMFT, enabling more accurate dynamical property calculations beyond the minimal two-site model.

Findings

Ground state energy errors below 0.01% for four-site models.

Accurate Green's functions obtained in intermediate to strong interactions.

Challenges in resolving low-energy spectral features in weak interactions.

Abstract

We present a variational quantum eigensolver (VQE) approach for solving the Anderson Impurity Model (AIM) arising in Dynamical Mean-Field Theory (DMFT). Recognizing that the minimal two-site approximation often fails to resolve essential spectral features, we investigate the efficacy of VQE for larger bath discretizations while adhering to near-term hardware constraints. We employ a symmetry-adapted ansatz enforcing conservation of particle number $(N)$, spin projection $(S_z=0)$, and total spin $(S^2=0)$ symmetry, benchmarking the performance against exact diagonalization across different interaction strengths using bath parameters extracted from the DMFT self-consistency loop. For a four-site model, the relative error in the ground state energy remains well below $0.01%$ with a compact parameter set $(N_p \le 30)$. Crucially, we demonstrate that the single-particle Green's function-the central quantity for DMFT-can be accurately extracted from VQE-prepared ground states via real-time evolution in the intermediate to strong interaction regimes. However, in the weak interaction regime, the Green's function exhibits noticeable deviations from the exact benchmark, particularly in resolving low-energy spectral features, despite the ground state energy showing excellent agreement. These findings demonstrate that VQE combined with real-time evolution can effectively extend quantum-classical hybrid DMFT beyond the two-site approximation, particularly for describing insulating phases. While this approach offers a viable pathway for simulating strongly correlated materials on near-term devices, the observation that accurate ground state energy does not guarantee accurate dynamical properties highlights a key challenge for applying such approaches to correlated metals.