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

By using the quantum computing the properties of hypernuclei ${}_{\mathrm{\Lambda }}^5$He, ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6$He and ${}_{\mathrm{\Lambda }}^9$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 ${}_{\mathrm{\Lambda }}^9$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.