Determining the ground and low-lying excited states is critical in numerous scenarios. Recent work has proposed the ancilla-entangled
variational quantum eigensolver (AEVQE) that utilizes entanglement between ancilla and physical qubits to simultaneously tagert multiple
low-lying energy levels. In this work, we report the experimental implementation of the AEVQE on a superconducting quantum cloud platform,
demonstrating the full procedure of solving the low-lying energy levels of the H molecule and the transverse-field Ising models (TFIMs). We
obtain the potential energy curves of H and show an indication of the ferromagnetic to paramagnetic phase transition in the TFIMs from the
average absolute magnetization. Moreover, we investigate multiple factors that affect the algorithmic performance and provide a comparison
with ancilla-free VQE algorithms. Our work demonstrates the experimental feasibility of the AEVQE algorithm and offers a guidance for the
VQE approach in solving realistic problems on publicly-accessible quantum platforms.
Link to the article is here.