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International Journal of Modern Physics B

A QUANTUM PERCEPTRON

M. Andrecut, Mazhar Ali

Published Feb 10, 2002• 5 citations
Publisher

Abstract

The task of a classical perceptron is to classify two classes of patterns by generating a separation hyperplane. Here, we give a complete description of a quantum perceptron. The quantum algorithms for classification and learning are formulated in terms of unitary quantum gates operators. In the quantum case, the concept of separable or non-separable classes is irrelevant because the quantum perceptron can learn a superposition of patterns which are not separable by a hyperplane.

DOI
10.1142/s0217979202009998

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The task of a classical perceptron is to classify two classes of patterns by generating a separation hyperplane. Here, we give a complete description of a quantum perceptron. The quantum algorithms for classification and learning are formulated in terms of unitary quantum gates operators. In the quantum case, the concept of separable or non-separable classes is irrelevant because the quantum perceptron can learn a superposition of patterns which are not separable by a hyperplane.
The classical perceptron describes an algorithm for supervised learning that considers only linearly separable problems in which groups can be separated by a line or hyperplane. A quantum perceptron can be used as building block of larger systems, it can process an arbitrary number of input vectors in parallel. This chapter presents a simple example of the quantum perceptron for two-dimensional input. The classical perceptron describes an algorithm for supervised learning that considers only linearly separable problems in which groups can be separated by a line or hyperplane. A quantum Perceptron can be used as building block of larger systems, it can process an arbitrary number of input vectors in parallel.
We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number of steps sublinear in the number of data points NNN, namely O(N)O(\sqrt{N})O(N​). The second algorithm illustrates how the classical mistake bound of O(1γ2)O(\frac{1}{γ^2})O(γ21​) can be further improved to O(1γ)O(\frac{1}{\sqrtγ})O(γ​1​) through quantum means, where γγγ denotes the margin. Such improvements are achieved through the application of quantum amplitude amplification to the version space interpretation of the perceptron model.
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementations of the quantum perceptron model have failed to fuse the two elegantly. This was due to a slow learning rule and a disregard for the unitary requirement. In this paper, we present a quantum perceptron that can compute functions uncomputable by the classical perceptron while analytically solving for parameters and preserving the unitary and dissipative requirements.
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we propose a quantum perceptron (QP) model that uses a reduced number of multi-qubit gates and is therefore less susceptible to quantum errors in current actual quantum computers with limited tolerance. The proposed quantum algorithm is superior to its classical counterpart, although since it does not take full advantage of quantum entanglement, it provides a lower encoding power than other quantum algorithms using multiple qubit entanglement. However, the use of separable-sate encoding allows for testing the algorithm and different training schemes at a large scale in currently available non-fault tolerant quantum computers. We demonstrate the performance of the proposed model by implementing a few qubits version of the QP in a simulated quantum computer. The proposed QP uses an N-ary encoding of the binary input data characterizing the patterns. We develop a hybrid (quantum-classical) training procedure for simulating the learning process of the QP and test their efficiency.
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.