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Brazilian Symposium on Neural Networks (SBRN)

A Weightless Neural Node Based on a Probabilistic Quantum Memory

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

Published Oct 1, 2010• 16 citations
Publisher

Abstract

The success of quantum computation is most commonly associated with speed up of classical algorithms, as the Shor's factoring algorithm and the Grover's search algorithm. But it should also be related with exponential storage capacity such as the super dense coding. In this work we use a probabilistic quantum memory proposed by Trugen berger, where one can store $\mathbf 2^n$ patterns with only $\mathbf n$ quantum bits (qbits). We define a new model of a quantum weightless neural node with this memory in a similar fashion as to the classical Random Access Memory (RAM) node is used in classical weightless neural networks. Some advantages of the proposed model are that the memory of the node does not grow exponentially with the number of inputs and that the node can generalise.

DOI
10.1109/sbrn.2010.52

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The success of quantum computation is most commonly associated with speed up of classical algorithms, as the Shor's factoring algorithm and the Grover's search algorithm. But it should also be related with exponential storage capacity such as the super dense coding. In this work we use a probabilistic quantum memory proposed by Trugen berger, where one can store 2n\mathbf 2^n2n patterns with only n\mathbf nn quantum bits (qbits). We define a new model of a quantum weightless neural node with this memory in a similar fashion as to the classical Random Access Memory (RAM) node is used in classical weightless neural networks. Some advantages of the proposed model are that the memory of the node does not grow exponentially with the number of inputs and that the node can generalise.
By exploiting the properties of superposition and entanglement found in quantum systems Quantum Computation has been applied to the design of algorithms considerably more efficient than the known classical ones. Known examples are the Shor's factoring algorithm and the Grover's search algorithm. This paper investigates the possibility of employing Quantum Computing techniques to the design of learning algorithms for neural networks tasks such as pattern recognition. We propose a quantum learning algorithm for neural networks where all patterns of the training set are presented concurrently in superposition. In the process we propose a novel model of a quantum weightless neural node. The algorithm is a combination of a quantum search algorithm, a probabilistic quantum memory and a quantum neural network.
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.
Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input.
Quantum Neural Network (QNN) is a young and outlying science built upon the combination of classical neural network and quantum computing. Making the best of some characteristics of the quantum operators, this paper presents both the network structure of Quantum Storage Network (QSN) and its corresponding pattern storage algorithm. QSN can store quantum patterns by a series of quantum unitary operators and its storage capacity or memory capacity is exponentially increased. Besides, the case analysis validates the feasibility and validity of the QSN proposed in this paper.