Evaluating the performance of sigmoid quantum perceptrons in quantum neural networks
Evaluating the performance of sigmoid quantum perceptrons in quantum neural networks
复制标题
评估量子神经网络中 S 型量子感知器的性能
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
M. Hartmann
中科院分区：
文献类型：
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作者：
Samuel A. Wilkinson;M. Hartmann
量子神经网络（QNN）被认为是一种有前景的量子机器学习架构。存在许多不同的量子电路设计被称为 QNN，但是没有明确的候选者表明自己比其他设计更合适。相反，对“量子感知器”——QNN 的基本构建模块——的探索仍在进行中。一种候选者是量子感知器，旨在模拟经典感知器的非线性激活函数。这种 sigmoid 量子感知器 (SQP) 继承了通用逼近特性，保证经典神经网络可以逼近任何函数。然而，这并不能保证由 SQP 构建的 QNN 比其经典对应物具有任何量子优势。在这里，我们通过计算 SQP 网络的有效维度和有效容量，以及检查它们在实际学习问题上的表现，批判性地研究 SQP 网络的能力和性能。将结果与其他缺乏激活函数的候选网络获得的结果进行比较。研究发现，更简单、显然更容易实现的参数量子电路实际上比 SQP 表现更好。这表明作为经典神经网络理论基石的万能逼近定理并不是 QNN 的相关标准。
Quantum neural networks (QNN) have been proposed as a promising architecture for quantum machine learning. There exist a number of different quantum circuit designs being branded as QNNs, however no clear candidate has presented itself as more suitable than the others. Rather, the search for a “quantum perceptron” – the fundamental building block of a QNN – is still underway. One candidate is quantum perceptrons designed to emulate the nonlinear activation functions of classical perceptrons. Such sigmoid quantum perceptrons (SQPs) inherit the universal approximation property that guarantees that classical neural networks can approximate any function. However, this does not guarantee that QNNs built from SQPs will have any quantum advantage over their classical counterparts. Here we critically investigate both the capabilities and performance of SQP networks by computing their effective dimension and effective capacity, as well as examining their performance on real learning problems. The results are compared to those obtained for other candidate networks which lack activation functions. It is found that simpler, and apparently easier-to-implement parametric quantum circuits actually perform better than SQPs. This indicates that the universal approximation theorem, which a cornerstone of the theory of classical neural networks, is not a relevant criterion for QNNs.
DOI：
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发表时间：
2006
期刊：
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影响因子：
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作者：
Iroon Polytechniou-
通讯作者：
Iroon Polytechniou-