Studying few cluster resonances with quantum neural network driven iterative Harrow-Hassidim-Lloyd algorithm

By using the quantum computing the properties of hypernuclei ${}^5_{\Lambda}$He, ${}^{\ 6}_{{\Lambda\Lambda}}$He and ${}^9_{\Lambda}$Be can be investigated within microscopic cluster model. Our approach combines quantum neural network (QNN) with iterative Harrow-Hassidim-Lloyd (IHHL) algorithm (abbreviated as QNN-IHHL) to solve the quantum many-body problem. To efficiently describe resonance phenomena, we employ complex scaling and eigenvector continuation techniques, providing a robust framework for identifying few-cluster resonance parameters within quantum computing. To validate our quantum algorithm, the resonant $4^{+}$ state of ${}^9_{\Lambda}$Be is chosen as a core example. With QNN-IHHL algorithm we realize a fully quantum workflow, which provides a novel framework and some ground work for exploring resonance properties in complex nuclear many-body systems.