Junyu Liu

Title: A grant unification theory of variational quantum algorithms

Abstract: We point out that the so-called quantum neural tangent kernel, the trace of Hessian matrix of the mean-square loss function, plays a significant role in the dynamics of variational quantum circuits in quantum machine learning algorithms. We summarize several perspectives of quantum neural tangent kernels, including overparametrization, symmetries, and phase transitions around and beyond the large-with limit of variational quantum circuits. We show that the study of quantum neural tangent kernels will uncover interesting, solvable, perturbative and non-perturbative behaviors in the gradient descent dynamics. Our studies open a new avenue for exploring quantum machine learning algorithms from the first principle, and designing variational quantum circuits for practical uses. (Based on https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.150601 and related works, and an ongoing project together with Bingzhi Zhang, Liang Jiang and Quntao Zhuang on non-perturbative phase transitions in quantum machine learning)