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Variational quantum circuits have been widely employed in quantum simulationand quantum machine learning in recent years. However, quantum circuits withrandom structures have poor trainability due to the exponentially vanishinggradient with respect to the circuit depth and the qubit number. This resultleads to a general standpoint that deep quantum circuits would not be feasiblefor practical tasks. In this work, we propose an initialization strategy withtheoretical guarantees for the vanishing gradient problem in general deepquantum circuits. Specifically, we prove that under proper Gaussian initializedparameters, the norm of the gradient decays at most polynomially when the qubitnumber and the circuit depth increase. Our theoretical results hold for boththe local and the global observable cases, where the latter was believed tohave vanishing gradients even for very shallow circuits. Experimental resultsverify our theoretical findings in the quantum simulation and quantumchemistry.

Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits