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

TL;DR

This paper introduces a hybrid quantum-classical solver using VQE for the Anderson impurity model, enabling Green's function reconstruction suitable for near-term quantum devices within DMFT frameworks.

Contribution

It develops a unified ansatz framework for impurity Green's function reconstruction using shallow quantum circuits, advancing quantum impurity solvers for strongly correlated materials.

Findings

Feasibility of Green's function reconstruction on near-term devices

Comparison of optimization routines for VQE convergence

Benchmarking against classical density of states calculations

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.