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Lecture notes in computer science

A Variational Algorithm for Quantum Single Layer Perceptron

Antonio Macaluso, Filippo Orazi, Matthias Klusch, Stefano Lodi, Claudio Sartori

Published Jan 1, 2023• 8 citations
Publisher
DOI
10.1007/978-3-031-25891-6_26

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The quantum perceptron, the variational circuit, and the Grover algorithm have been proposed as promising components for quantum machine learning. This paper presents a new quantum perceptron that combines the quantum variational circuit and the Grover algorithm. However, this does not guarantee that this quantum variational perceptron with Grover's algorithm (QVPG) will have any advantage over its quantum variational (QVP) and classical counterparts. Here, we examine the performance of QVP and QVP-G by computing their loss function and analyzing their accuracy on the classification task, then comparing these two quantum models to the classical perceptron (CP). The results show that our two quantum models are more efficient than CP, and our novel suggested model QVP-G outperforms the QVP, demonstrating that the Grover can be applied to the classification task and even makes the model more accurate, besides the unstructured search problems.
In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv:1809.06056 (2018). In detail, we show that in the first part of the training of the variational quantum perceptron, the quantum coherence of the total system is concentrated in the index register and in the second part, the Grover algorithm consumes the quantum coherence in the index register. This implies that the quantum coherence distribution and the quantum coherence depletion are required in the training of variational quantum perceptron. In addition, we investigate the behavior of entanglement during the training of variational quantum perceptron. We show that the bipartite concurrence between feature and index register decreases since Grover operation is only performed on the index register. Also, we reveal that the concurrence between the two qubits of index register increases as the variational quantum perceptron is trained.
There are numerous models of quantum neural networks that have been applied to variegated problems such as image classification, pattern recognition etc.Quantum inspired algorithms have been relevant for quite awhile. More recently, in the NISQ era, hybrid quantum classical models have shown promising results. Multi-feature regression is common problem in classical machine learning. Hence we present a comparative analysis of continuous variable quantum neural networks (Variational circuits) and quantum backpropagating multi layer perceptron (QBMLP). We have chosen the contemporary problem of predicting rise in COVID-19 cases in India and USA. We provide a statistical comparison between two models , both of which perform better than the classical artificial neural networks.