Knowledge distillation inspired variational quantum eigensolver with virtual annealing

In this paper, we propose a knowledge distillation inspired variational quantum eigensolver (KD-VQE). Inspired by the virtual distillation process in KD, KD-VQE introduces a virtual annealing mechanism to the VQE framework. In KD-VQE, measurement resources (shots) are dynamically allocated among multiple trial wavefunctions, each weighted according to a Boltzmann distribution with a virtual temperature. As the temperature decreases gradually, the algorithm progressively reallocates resources toward lower-energy candidates, effectively filtering out suboptimal states and steering the system toward the global minimum. We demonstrate the effectiveness of KD-VQE through numerical simulations on the two-site Fermi–Hubbard model and the one-dimensional hydrogen chain. Compared to conventional VQE, KD-VQE shows improved convergence and reduced sensitivity to poor initializations.