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

Mukherjee, Anirban
Berthusen, Noah F.
Getelina, João C.
Orth, Peter
Yao, Yong-Xin
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Orth, Peter
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Physics and Astronomy
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Ames Laboratory
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Physics and Astronomy
We perform a systematic study of preparing ground states of correlated eg and t2g multi-orbital impurity models using variational quantum eigensolvers (VQEs). Both xed and adaptive wavefunction ans atze are considered and the resulting gate depths and performance with and without quantum sampling noise are analyzed. We investigate the qubit adaptive derivative-assembled pseudo-trotter (ADAPT) VQE approach in the Hartree-Fock orbital basis, as well as the Hamiltonian variational ansatz (HVA) and an adaptive variant of it in the atomic orbital basis. An operator pool composed of pairwise commutators of the Hamiltonian terms is developed to allow a fair comparison between the adaptive and the xed HVA ansatz. Using statevector simulations, we show that the most compact ans atze are obtained in the atomic orbital representation with symmetry-based Pauli tapering in parity encoding. We further perform adaptive VQE calculations including sampling noise, and demonstrate that high- delity state preparation can be achieved with the Hamiltonian commutator pool. By utilizing a doubly decomposed form of the impurity Hamiltonian and a noise resilient optimizer, we show that this approach requires only a modest number of about 212 samples per energy evaluation. We discover a dichotomy of the operator pool complexity in the presence of quantum noise, where a small pool size reduces the adaptive overhead but a larger pool size accelerates the convergence to the ground state. Finally, we measure the ground state energy of the eg model on IBM quantum hardware using the converged qubit-ADAPT ansatz, and obtain a relative error of 0.7% using error mitigation techniques including symmetry- ltering and zero-noise extrapolation.
This is a pre-print of the article Mukherjee, Anirban, Noah F. Berthusen, João C. Getelina, Peter P. Orth, and Yong-Xin Yao. "Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models." arXiv preprint arXiv:2203.06745 (2022). DOI: 10.48550/arXiv.2203.06745. Copyright 2022 The Authors. Posted with permission.