Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.

中文翻译：

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量子神经网络训练景观中的贫瘠高原。

对于嘈杂的中级量子设备的许多实验建议都涉及使用经典的优化循环来训练参数化的量子电路。这种混合量子经典算法在量子模拟，优化和机器学习中的应用很受欢迎。由于其简单性和硬件效率，经常提出随机电路作为探索量子态空间的初步猜测。我们证明了希尔伯特空间的指数维数和梯度估计复杂度使得该选择不适合运行在多个量子位以上的混合量子经典算法。具体来说，我们表明对于大量合理的参数化量子电路，沿任何合理方向的梯度从零到某个固定精度的概率根据量子位的数量呈指数减小。我们认为这与随机电路的2设计特征有关，因此必须研究该问题的解决方案。