Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits
This addresses a critical trainability issue for quantum machine learning practitioners, enabling deeper circuits for practical tasks, though it is incremental as it builds on known initialization methods.
The paper tackles the vanishing gradient problem in deep variational quantum circuits by proposing a Gaussian initialization strategy, proving that gradient norms decay polynomially rather than exponentially with qubit number and circuit depth, and validating this with experiments in quantum simulation and chemistry.
Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks. In this work, we propose an initialization strategy with theoretical guarantees for the vanishing gradient problem in general deep quantum circuits. Specifically, we prove that under proper Gaussian initialized parameters, the norm of the gradient decays at most polynomially when the qubit number and the circuit depth increase. Our theoretical results hold for both the local and the global observable cases, where the latter was believed to have vanishing gradients even for very shallow circuits. Experimental results verify our theoretical findings in the quantum simulation and quantum chemistry.