  Variational quantum algorithms (VQAs) have recently received significant
attention from the research community due to their promising performance in
Noisy Intermediate-Scale Quantum computers (NISQ). However, VQAs run on
parameterized quantum circuits (PQC) with randomly initialized parameters are
characterized by barren plateaus (BP) where the gradient vanishes exponentially
in the number of qubits. In this paper, we first review quantum natural
gradient (QNG), which is one of the most popular algorithms used in VQA, from
the classical first-order optimization point of view. Then, we proposed a
\underline{L}ook \underline{A}round \underline{W}arm-\underline{S}tart QNG
(LAWS) algorithm to mitigate the widespread existing BP issues. LAWS is a
combinatorial optimization strategy taking advantage of model parameter
initialization and fast convergence of QNG. LAWS repeatedly reinitializes
parameter search space for the next iteration parameter update. The
reinitialized parameter search space is carefully chosen by sampling the
gradient close to the current optimal. Moreover, we present a unified framework
(WS-SGD) for integrating parameter initialization techniques into the
optimizer. We provide the convergence proof of the proposed framework for both
convex and non-convex objective functions based on Polyak-Lojasiewicz (PL)
condition. Our experiment results show that the proposed algorithm could
mitigate the BP and have better generalization ability in quantum
classification problems.
