Regensburg 2022 – scientific programme

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QI: Fachverband Quanteninformation

QI 6: Quantum Information: Concepts and Methods

QI 6.5: Talk

Tuesday, September 6, 2022, 10:45–11:00, H9

Evaluating the power and performance of sigmoid quantum perceptrons. — •Samuel Wilkinson and Michael Harman — Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstr. 7, 91058 Erlangen, Germa

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) inherent the universal approximation property that guarantees that classical neural networks can approximate any continuous 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 general measures of the dimension and capacity of the network, as well as its 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, 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.