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, H2 molecule, and strongly correlated planar H4 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.
Highlights
Quantum computing (QC) techniques attract much attention in many mathematics, physics, and chemistry areas by providing means to address insurmountable computational barriers for simulating quantum systems on classical computers.[2, 3, 43, 47, 53, 61] One of the focus areas for quantum computing is quantum chemistry, where Hamiltonians can be effectively mapped into qubit registers
Several quantum computing algorithms, including quantum phase estimator (QPE) [5, 12, 15, 26, 38, 52, 58, 69] and variational quantum eigensolver (VQE), [16, 24, 29, 31, 32, 44, 50, 55, 60] have been extensively tested on benchmark systems corresponding to the description of chemical reactions involving bond-forming and breaking processes, excited states, and strongly correlated molecular systems
We will test its performance, in particular the performance of the more affordable lower order PDS(K)-VQS (K = 2, 3, 4) approaches combining with the trial wave function expressed in low-depth quantum circuits, at finding the ground state and its energy for the Hamiltonians describing toy models and H2 molecular system, as well as the strongly correlated planar H4 system, in some challenging situations where the barren plateau problem precludes the effective utilization of the standard VQE approach
Summary
A typical way of addressing these challenges in VQE approaches is by incorporating more and more parameters (usually corresponding to excitation amplitudes in a broad class of unitary coupledcluster methods [4, 17, 27, 35, 37, 64]) This brute force approach is quickly stumbling into insurmountable problems associated with the resulting quantum circuit com-. We will test its performance, in particular the performance of the more affordable lower order PDS(K)-VQS (K = 2, 3, 4) approaches combining with the trial wave function expressed in low-depth quantum circuits, at finding the ground state and its energy for the Hamiltonians describing toy models and H2 molecular system, as well as the strongly correlated planar H4 system, in some challenging situations where the barren plateau problem precludes the effective utilization of the standard VQE approach
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