Expressibility and Trainability Analysis of Hardware-Efficient Ansatz Variants in Variational Quantum Eigensolver with a Linear Mixing Model

provide a more stable gradient distribution and more consistent optimization performance. These findings are consistent with the proposed linear mixing expressibility-trainability model, states that increased expressibility is not always directly proportional to the ease of the optimization process; homogenization of the state space actually reduces the directional information needed by the optimizer. These results provide an important basis for selecting more effective ansatzes in future implementations of variational quantum algorithms.