Knowledge Distillation Inspired Variational Quantum Eigensolver with Virtual Annealing

TL;DR

This paper introduces KD-VQE, a novel quantum algorithm inspired by knowledge distillation and virtual annealing, which dynamically allocates measurement resources to improve convergence to the ground state in quantum chemistry problems.

Contribution

The paper presents KD-VQE, integrating virtual annealing into VQE to enhance resource allocation and convergence, a novel approach inspired by knowledge distillation techniques.

Findings

KD-VQE achieves better convergence than standard VQE.

KD-VQE explores a broader solution space.

KD-VQE demonstrates improved reliability in finding ground states.

Abstract

In this paper, we propose a Knowledge Distillation Inspired Variational Quantum Eigensolver (KD-VQE). Inspired by the virtual distillation process in knowledge distillation (KD), KD-VQE introduces a virtual annealing mechanism to the variational quantum eigensolver (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. Moreover, we demonstrate the effectiveness of KD-VQE by applying it to the two-site Fermi-Hubbard model. Compared to standard VQE framework, KD-VQE explores a broader region of the solution space, and offers improved convergence behavior and increased reliability.