Variational quantum solver employing the PDS energy functional

Bo Peng and Karol Kowalski

Physical and Computational Science Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States of America

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Abstract

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H$_2$ molecule, and strongly correlated planar H$_4$ system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

In this paper, we developed a new effective cost function for the variational quantum solver, which in principle can not only help avoid some Barren Plateaus, but also converge to ground state energies outside of the ansatz class, and thus outperforms the conventional one in some challenging cases.

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[3] Edgar Andres Ruiz Guzman and Denis Lacroix, "Predicting ground state, excited states and long-time evolution of many-body systems from short-time evolution on a quantum computer", arXiv:2104.08181.

[4] Daniel Claudino, Alexander J. McCaskey, and Dmitry I. Lyakh, "A backend-agnostic, quantum-classical framework for simulations of chemistry in C++", arXiv:2105.01619.

The above citations are from SAO/NASA ADS (last updated successfully 2021-09-23 05:38:03). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2021-09-23 05:38:01).