Understanding strongly correlated materials presents a significant challenge in condensed matter physics, often requiring computationally intensive methods like dynamical mean‑field theory (DMFT). A major limitation within DMFT lies in the difficulty of solving the Anderson impurity model (AIM), particularly as the system size increases. Mariia Karabin, Tanvir Sohail, and Dmytro Bykov, alongside colleagues from Middle Tennessee State University and Oak Ridge National Laboratory, have addressed this problem by developing a novel classical‑hybrid solver based on the variational eigensolver (VQE). This research demonstrates the potential for reconstructing the impurity Green’s function using shallow quantum circuits, offering a pathway towards practical implementation on near‑term quantum devices and establishing crucial benchmarks for future impurity solvers integrated within DMFT calculations.

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Quantum Solver for Dynamical Mean‑Field Theory

Quantum embedding methods, such as dynamical mean‑field theory (DMFT), offer a powerful framework for investigating strongly correlated materials. A central computational bottleneck within DMFT lies in solving the Anderson impurity model (AIM), the exact solution of which is classically intractable for large bath sizes. This work details the development and benchmarking of a quantum‑classical hybrid solver specifically tailored for DMFT applications. The solver utilises the variational quantum eigensolver (VQE) to prepare the ground state of the AIM employing shallow quantum circuits. The approach centres on a unified ansatz framework designed to efficiently prepare the ground‑state wavefunction.

This allows for a systematic exploration of the parameter space and optimisation of the VQE circuit. Benchmarking is performed against established classical methods to assess the accuracy and scalability of the hybrid solver. Results demonstrate the potential for significant speed‑ups in solving the AIM, particularly for systems where classical methods struggle. Specific contributions include a novel implementation of the VQE algorithm adapted for the AIM within the DMFT framework. The unified ansatz provides increased flexibility and control over the quantum circuit construction. Furthermore, the research establishes a clear pathway towards leveraging near‑term quantum devices for tackling challenging problems in strongly correlated materials. This hybrid quantum‑classical approach represents a significant step towards overcoming the computational limitations currently hindering progress in the field.

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Dynamical Mean‑Field Theory and Anderson Impurity Models

Research focuses on improving methods for understanding the complex behaviour of interacting electrons in materials, a fundamental problem in both chemistry and condensed‑matter physics. Direct numerical solutions to the Schrödinger equation are often impossible for realistic systems, necessitating approximation techniques. Density functional theory is a common approach, but struggles with strong electron correlations, particularly in materials exhibiting Mott physics or dynamic electron localisation. To address these limitations, scientists are augmenting density functional theory with dynamical mean‑field theory (DMFT).

DMFT maps a lattice model onto a local Anderson impurity model (AIM), capturing local dynamical fluctuations and becoming exact in infinite dimensions. Solving the AIM within DMFT traditionally requires computationally intensive techniques, motivating the development of more efficient quantum methods. This work explores a novel approach using parameter‑shifted quantum circuits to extract information about particle and hole excitations from the ground state. The method reconstructs the impurity Green’s function using a continued‑fraction expansion, allowing for analysis of the density of states (DOS).

Performance was evaluated with varying bath sizes and interaction strengths, under realistic noisy conditions simulating near‑term quantum devices. The researchers compared the convergence and fidelity of three optimisation routines—COBYLA, Adam, and L‑BFGS‑B—and assessed the benefits of incorporating a quantum‑computed moment (QCM) correction to variational energies. Reconstructed DOS results were benchmarked against those obtained using classical computational pipelines, demonstrating the feasibility of Green’s‑function reconstruction on current quantum hardware and establishing practical benchmarks for quantum impurity solvers within DMFT loops.

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Variational Quantum Eigensolver Solves Anderson Impurity Model

Scientists achieved a breakthrough in solving the Anderson impurity model (AIM), a central challenge in dynamical mean‑field theory (DMFT) used for investigating strongly correlated materials. The team developed and benchmarked a classical‑quantum hybrid solver utilising the variational quantum eigensolver (VQE) to prepare the ground state of the AIM with shallow quantum circuits. This innovative approach circumvents the classical intractability of solving the AIM for large bath sizes, offering a pathway to more accurate simulations of complex materials. Experiments revealed the feasibility of reconstructing the impurity Green’s function, a crucial step in DMFT calculations, on near‑term quantum devices.

The solver employs a unified ansatz framework to prepare both particle and hole excitations from the ground state using parameter‑shifted circuits. Data shows successful reconstruction of the density of states (DOS) against results obtained from a classical pipeline, validating the quantum approach. Tests prove the solver’s performance across varying bath sizes and interaction strengths, even under noisy, shot‑limited conditions typical of current quantum hardware. The research meticulously compared three optimisation routines—COBYLA, Adam, and L‑BFGS‑B—assessing their convergence and fidelity. Results demonstrate that incorporating a quantum‑computed moment (QCM) correction to the variational energies significantly improves accuracy.

Specifically, the team evaluated performance across multiple bath sizes and interaction strengths, establishing practical benchmarks for quantum impurity solvers within self‑consistent DMFT loops. Measurements confirm the ability to accurately represent the complex quantum states necessary for modelling strongly correlated electron systems. Furthermore, the study details the computational overhead associated with each optimisation strategy, providing realistic expectations for embedding this quantum solver into full DMFT workflows. The breakthrough delivers a minimal yet expressive variational ansatz capable of preparing both ground and excited states, minimising the required quantum circuit depth. This work establishes a foundation for future advancements in quantum‑enhanced materials modelling and opens possibilities for simulating increasingly complex systems previously inaccessible to classical methods.

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Hybrid Solver Reconstructs Impurity Green’s Function

This research presents a novel quantum‑classical hybrid solver designed to address a key limitation within dynamical mean‑field theory: the intractable nature of solving the Anderson impurity model for realistically sized systems. By employing the variational eigensolver with shallow quantum circuits, the authors successfully demonstrate the feasibility of reconstructing the impurity Green’s function, a crucial step in DMFT calculations. The approach utilises a unified ansatz framework to prepare both ground and excited states, alongside a continued‑fraction expansion technique for Green’s‑function reconstruction. The study establishes practical benchmarks for quantum impurity solvers intended for integration into self‑consistent DMFT loops, showing performance across varying bath sizes and interaction strengths even under noisy conditions typical of near‑term quantum devices.

Evaluations of different optimisation routines—COBYLA, Adam, and L‑BFGS‑B—alongside the incorporation of moment‑based energy corrections, contribute to a refined methodology for variational energy estimation. The authors acknowledge limitations stemming from the finite bath sizes explored and the inherent noise present in current quantum hardware. Future work will focus on integrating this quantum impurity solver more fully within complete DMFT workflows, further assessing its capabilities and scalability for tackling increasingly complex strongly correlated materials, potentially unlocking new insights into their behaviour. The demonstrated ability to reconstruct Green’s functions on near‑term devices represents a significant step towards leveraging quantum computation for materials science.

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Reference

ArXiv: Quantum solver for single‑impurity Anderson models with particle‑hole symmetry – https://arxiv.org/abs/2601.10594