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

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 $0.7\%$.

18 pages, 9 figures

References in corpus (8)

• Simulated Quantum Computation of Molecular Energies
• Strong electronic correlations from Hund's coupling
• Correlated Topological Insulators with Mixed Valence
• Quantum embedding theories
• Equivalence of Gutzwiller and slave-boson mean-field theories for multi-band Hubbard models
• Gutzwiller description of non-magnetic Mott insulators: a dimer lattice model
• LDA+Gutzwiller Method for Correlated Electron Systems
• Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model

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• Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
• Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models