Quantum-Classical Embedding via Ghost Gutzwiller Approximation for Enhanced Simulations of Correlated Electron Systems

TL;DR

This paper introduces a quantum-classical embedding method based on the ghost Gutzwiller approximation to improve simulations of correlated electron systems on quantum hardware, addressing resource limitations and noise effects.

Contribution

It develops a novel embedding framework enabling quantum-enhanced simulations of ground-state and spectral properties of correlated materials, with practical error mitigation strategies.

Findings

Circuit depth increases with ghost mode number, from 16 to 104.

Iceberg quantum error detection reduces errors by up to 40%.

Benchmarking on IBM and Quantinuum hardware shows promising results.

Abstract

Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems onto effective impurity models, allowing more feasible simulations on pre- and early-fault-tolerant quantum devices. This work develops a quantum-classical embedding framework based on the ghost Gutzwiller approximation to enable quantum-enhanced simulations of ground-state properties and spectral functions of correlated electron systems. Circuit complexity is analyzed using an adaptive variational quantum algorithm on a statevector simulator, applied to the infinite-dimensional Hubbard model with increasing ghost mode numbers from 3 to 5, resulting in circuit depths growing from 16 to 104. Noise effects are examined using a realistic error model, revealing significant impact on the spectral weight of the Hubbard bands. To mitigate these effects, the Iceberg quantum error detection code is employed, achieving up to 40% error reduction in simulations. Finally, the accuracy of the density matrix estimation is benchmarked on IBM and Quantinuum quantum hardware, featuring distinct qubit-connectivity and employing multiple levels of error mitigation techniques.