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arXiv · 2109.00288

Exploring variational quantum eigensolver ansatzes for the long-range XY model

Jia-Bin You·Dax Enshan Koh·Jian Feng Kong·Wen-Jun Ding·Ching Eng Png·Lin Wu
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Abstract

Finding the ground state energy and wavefunction of a quantum many-body system is a key problem in quantum physics and chemistry. We study this problem for the long-range XY model by using the variational quantum eigensolver (VQE) algorithm. We consider VQE ansatzes with full and linear entanglement structures consisting of different building gates: the CNOT gate, the controlled-rotation (CRX) gate, and the two-qubit rotation (TQR) gate. We find that the full-entanglement CRX and TQR ansatzes can sufficiently describe the ground state energy of the long-range XY model. In contrast, only the full-entanglement TQR ansatz can represent the ground state wavefunction with a fidelity close to one. In addition, we find that instead of using full-entanglement ansatzes, restricted-entanglement ansatzes where entangling gates are applied only between qubits that are a fixed distance from each other already suffice to give acceptable solutions. Using the entanglement entropy to characterize the expressive powers of the VQE ansatzes, we show that the full-entanglement TQR ansatz has the highest expressive power among them.

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Jia-Bin You, Dax Enshan Koh, Jian Feng Kong, Wen-Jun Ding, Ching Eng Png, Lin Wu. 2021-09-01. Exploring variational quantum eigensolver ansatzes for the long-range XY model. https://doi.org/10.1038/s41598-026-46651-2

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