Quantum solver for single-impurity Anderson models with particle-hole symmetry

TL;DR

This work addresses the challenge of solving the Anderson impurity model within DMFT on near-term quantum hardware by deploying a quantum-classical hybrid solver that uses a variational quantum eigensolver to prepare the AIM ground state with a symmetry-constrained, shallow ansatz and to generate particle/hole excitations for Green's function reconstruction. Green's functions are obtained via a Krylov-based continued-fraction expansion, with the impurity DOS benchmarked against classical exact results across bath sizes $N_b\in\{1,3,5\}$ and Hubbard interactions $U$, while three optimizers (COBYLA, Adam, L-BFGS-B) and a quantum-computed-moments (QCM) correction are explored to quantify accuracy-cost trade-offs. Key contributions include the demonstration that near-term devices can reconstruct real-frequency observables with reasonable fidelity, a systematic comparison of optimization strategies under sampling noise, and a quantification of the resource overheads for integrating quantum impurity solvers into DMFT loops. The findings establish practical benchmarks and pave the way for extended DMFT/DFT+DMFT workflows leveraging quantum impurity solvers, while emphasizing the role of error mitigation and higher-moment corrections in achieving robust performance.

Abstract

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM), whose exact solution is classically intractable for large bath sizes. In this work, we develop and benchmark a quantum-classical hybrid solver tailored for DMFT applications, using the variational quantum eigensolver (VQE) to prepare the ground state of the AIM with shallow quantum circuits. The solver uses a unified ansatz framework to prepare the particle and hole excitations of the ground-state from parameter-shifted circuits, enabling the reconstruction of the impurity Green's function through a continued-fraction expansion. We evaluate the performance of this approach across a few bath sizes and interaction strengths under noisy, shot-limited conditions. We compare three optimization routines (COBYLA, Adam, and L-BFGS-B) in terms of convergence and fidelity, assess the benefits of estimating a quantum-computed moment (QCM) correction to the variational energies, and benchmark the approach by comparing the reconstructed density of states (DOS) against that obtained using a classical pipeline. Our results demonstrate the feasibility of Green's function reconstruction on near-term devices and establish practical benchmarks for quantum impurity solvers embedded within self-consistent DMFT loops.

Figures (8)

• Figure 1: Spin-block ordering used to map the model’s spin-up and down sites onto a linear chain of qubits.
• Figure 2: Half-filling (top left) and Givens rotation (top right) gates used to construct ansatz for the ground states of single-impurity AIMs. Ansatz for the ground states of single-impurity AIMs with one (bottom left) and three (bottom right) bath sites.
• Figure 3: Ansatz for the particle (right) and hole (left) excitations of single-bath AIM ground-states preparing states with spin projection $S_z=\tfrac{1}{2}$ (top) and $S_z=-\tfrac{1}{2}$ (bottom).
• Figure 4: Absolute relative error between the exact ground-state energy and its variational estimate. For impurity models with five bath sites, the proposed ansatz yields energy estimates accurate to within about five percent of the exact ground-state energy.
• Figure 5: Absolute relative error between variational energies from simulations with and without sampling noise. These simulations solved AIMs with one (top) and three (bottom) bath sites and on-site energy $U=2$. The shown mean values and standard deviations result from simulations initiated from ten distinct starting points, each repeated five times to account for sampling errors.