论文标题
通过高斯初始化在深度变化量子电路中从贫瘠的高原逃脱
Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits
论文作者
论文摘要
近年来，变异量子电路已被广泛用于量子模拟和量子机学习。但是，由于相对于电路深度和量子数的梯度呈指数呈指数消失的梯度，因此具有随机结构的量子电路的训练性较差。这一结果导致一般的观点，即深量子电路对于实际任务是不可行的。在这项工作中，我们提出了一种初始化策略，并在一般深度量子电路中为消失的梯度问题提供了理论保证。具体而言，我们证明，在适当的高斯初始化参数下，当量子数和电路深度增加时，梯度的规范最多地衰减。我们对本地和全球可观察情况的理论结果都构成，因为后者被认为甚至在非常浅的电路中都具有消失的梯度。实验结果验证了我们在量子模拟和量子化学中的理论发现。
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.
