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Variational quantum algorithms (VQAs) have recently received significantattention from the research community due to their promising performance inNoisy Intermediate-Scale Quantum computers (NISQ). However, VQAs run onparameterized quantum circuits (PQC) with randomly initialized parameters arecharacterized by barren plateaus (BP) where the gradient vanishes exponentiallyin the number of qubits. In this paper, we first review quantum naturalgradient (QNG), which is one of the most popular algorithms used in VQA, fromthe 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 acombinatorial optimization strategy taking advantage of model parameterinitialization and fast convergence of QNG. LAWS repeatedly reinitializesparameter search space for the next iteration parameter update. Thereinitialized parameter search space is carefully chosen by sampling thegradient close to the current optimal. Moreover, we present a unified framework(WS-SGD) for integrating parameter initialization techniques into theoptimizer. We provide the convergence proof of the proposed framework for bothconvex and non-convex objective functions based on Polyak-Lojasiewicz (PL)condition. Our experiment results show that the proposed algorithm couldmitigate the BP and have better generalization ability in quantumclassification problems.

LAWS: Look Around and Warm-Start Natural Gradient Descent for Quantum Neural Networks