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Brazilian Symposium on Neural Networks (SBRN)

On the Universality of Quantum Logical Neural Networks

Adenilton José da Silva, Teresa B. Ludermir, Wilson Rosa de Oliveira

Published Oct 1, 2012• 7 citations
Publisher

Abstract

In this paper we investigate the computational power of the quantum weightless neural networks (q-WNN) and propose a novel quantum weightless neural node. The new quantum neuron is derived from the quantum probabilistic logic node (qPLN), which is a mathematical quantisation of the weightless neural node PLN. By a slight modification on the input lines of the qPLN node it is possible to define the quantum psi-neuron. We show in this paper that psi-neurons can be used to approximate any quantum circuit.

DOI
10.1109/sbrn.2012.44

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In this paper we investigate the computational power of the quantum weightless neural networks (q-WNN) and propose a novel quantum weightless neural node. The new quantum neuron is derived from the quantum probabilistic logic node (qPLN), which is a mathematical quantisation of the weightless neural node PLN. By a slight modification on the input lines of the qPLN node it is possible to define the quantum psi-neuron. We show in this paper that psi-neurons can be used to approximate any quantum circuit.
Quantum analogues of the (classical) Logical Neural Networks (LNN) models are proposed in (q-LNN for short). We shall here further develop and investigate the q-LNN composed of the quantum analogue of the Probabilistic Logic Node (PLN) and the multiple-valued PLN (MPLN) variations, dubbed q-PLN and q-MPLN respectively. Besides a clearer mathematical description, we present a computationally efficient and simply described quantum learning algorithm in contrast to what has been proposed to the quantum weighted version.
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Quantum computing enables quantum neural networks (QNNs) to have great potential to surpass artificial neural networks. The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various models related to QNNs have been developed, they are facing the challenge of merging the nonlinear, dissipative dynamics of neural computing into the linear, unitary quantum system. In this paper, we establish different quantum circuits to approximate nonlinear functions and then propose a generalizable framework to realize any nonlinear quantum neuron. We present two quantum neuron examples based on the proposed framework. The quantum resources required to construct a single quantum neuron are polynomial in function of the input size. Finally, both IBM Quantum Experience results and numerical simulations illustrate the effectiveness of the proposed framework.