Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models

TL;DR

This study compares various adaptive variational quantum eigensolvers for multi-orbital impurity models, demonstrating high-fidelity ground state preparation and analyzing hardware noise effects, advancing quantum simulation capabilities.

Contribution

It provides a systematic comparison of adaptive VQEs for multi-orbital models, including experimental results on quantum hardware and noise robustness analysis.

Findings

Achieved >99.9% fidelity with ~2^14 shots per measurement.

Parameter optimization remains feasible with two-qubit gate errors below 10^-3.

Measured ground state energy with 0.7% relative error on IBM and Quantinuum hardware.

Abstract

Hybrid quantum-classical embedding methods for correlated materials simulations provide a path towards potential quantum advantage. However, the required quantum resources arising from the multi-band nature of $d$ and $f$ electron materials remain largely unexplored. Here we compare the performance of different variational quantum eigensolvers in ground state preparation for interacting multi-orbital embedding impurity models, which is the computationally most demanding step in quantum embedding theories. Focusing on adaptive algorithms and models with 8 spin-orbitals, we show that state preparation with fidelities better than $99.9\%$ can be achieved using about $2^{14}$ shots per measurement circuit. When including gate noise, we observe that parameter optimizations can still be performed if the two-qubit gate error lies below $10^{-3}$, which is slightly smaller than current hardware levels. Finally, we measure the ground state energy on IBM and Quantinuum hardware using a converged adaptive ansatz and obtain a relative error of $0.7\%$.