International Journal of Circuit Theory and Applications

Neural networks with quantum architecture and quantum learning

Massimo Panella, Giuseppe Martinelli

Published Jul 23, 2009• 75 citations

Abstract

Abstract A method is proposed for solving the two key problems facing quantum neural networks: introduction of nonlinearity in the neuron operation and efficient use of quantum superposition in the learning algorithm. The former is indirectly solved by using suitable Boolean functions. The latter is based on the use of a suitable nonlinear quantum circuit. The resulting learning procedure does not apply any optimization method. The optimal neural network is obtained by applying an exhaustive search among all the possible solutions. The exhaustive search is carried out by the proposed quantum circuit composed of both linear and nonlinear components. Copyright © 2009 John Wiley & Sons, Ltd.

DOI: 10.1002/cta.619

Related papers

Neurofuzzy Networks With Nonlinear Quantum Learning

Massimo Panella, Giovanni Martinelli

Nonlinear quantum processing allows the solution of an optimization problem by the exhaustive search on all its possible solutions. Hence, it can replace advantageously the algorithms for learning from a training set. In order to pursue this possibility in the case of neurofuzzy networks, we propose in this paper to tailor their architectures to the requirements of quantum processing. In particular, superposition is introduced to pursue parallelism and entanglement to associate the network performance with each solution present in the superposition. Two aspects of the proposed method are considered in detail: the binary structure of membership functions and fuzzy reasoning and the use of a particular nonlinear quantum algorithm for extracting the optimal neurofuzzy network by exhaustive search.

IEEE Transactions on Fuzzy SystemsMar 9, 200939 citations

Artificial neural network architecture selection in a quantum computer

Adenilton José da Silva

Miniaturisation of computers components is taking us from classical to quantum physics domain. Further reduction in computer components size eventually will lead to the development of computer systems whose components will be on such a small scale that quantum physics intrinsic properties must be taken into account. The expression quantum computation and a first formal model of a quantum computer were first employed in the eighties. With the discovery of a quantum algorithm for factoring exponentially faster than any known classical algorithm in 1997, quantum computing began to attract industry investments for the development of a quantum computer and the design of novel quantum algorithms. For instance, the development of learning algorithms for neural networks. Some artificial neural networks models can simulate an universal Turing machine, and together with learning capabilities have numerous applications in real life problems. One limitation of artificial neural networks is the lack of an efficient algorithm to determine its optimal architecture. The main objective of this work is to verify whether we can obtain some advantage with the use of quantum computation techniques in a neural network learning and architecture selection procedure. We propose a quantum neural network, named quantum perceptron over a field (QPF). QPF is a direct generalisation of a classical perceptron which addresses some drawbacks found in previous models for quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimises the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures and neural networks parameters in linear time over the number of examples in the training set. SAL is the first quantum learning algorithm to determine neural network architectures in linear time. This speedup is obtained by the use of quantum parallelism and a non linear quantum operator.

Jun 26, 20150 citations

Quantum-Inspired Optimization of Neural Network Architecture

Jincheng Zhang

This paper explores a novel approach to neural network architecture optimization inspired by quantum superposition and measurement. Traditional neural network architecture search methods, such as reinforcement learning or evolutionary algorithms, often suffer from computational bottlenecks and slow convergence rates. We propose a genetic algorithm that leverages quantum-inspired probability amplitudes to represent and evaluate neural network architectures. Each architecture is assigned a set of probability amplitudes, reflecting the potential for success. Through a simulated measurement process, the algorithm dynamically adjusts these amplitudes, favoring architectures with higher potential and accelerating the search for optimal configurations. The core idea is that quantum superposition allows us to explore a vast solution space concurrently, while the measurement process mimics the collapse of the wave function, focusing the search on promising candidates. This approach demonstrates the potential to significantly reduce the time and resources required for neural network architecture design, paving the way for more efficient and powerful deep learning models. We present a detailed theoretical framework and outline the key components of the algorithm, emphasizing its ability to mimic quantum phenomena for architectural optimization.

Aug 31, 20260 citations

Nonlinear quantum neuron: A fundamental building block for quantum neural networks

Shilu Yan, Hongsheng Qi, Wei Cui

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.

arXiv:2011.03429Physical Review ANov 25, 202046 citations

A learning algorithm for quantum neuron

Li Fei, Xiaoliang Dong, Shengmei Zhao +1 more

Most proposals for quantum neural networks (QNN) have skipped over the problem of how to learn the networks. This paper describes a novel model for quantum neuron and proposes its learning algorithm. It can be shown that this algorithm works on quantum systems and the convergence result demonstrates efficient performance of the proposed quantum neuron. Numerical and graphical results show that this single quantum neuron can perform the XOR function unrealizable with a classical neuron and can eliminate the necessity of building a network of neurons to obtain nonlinear mapping.

International Conference on Signal ProcessingJun 28, 20054 citations

Quantum Neuron: an elementary building block for machine learning on quantum computers

Yudong Cao, Gian Giacomo Guerreschi, Alán Aspuru‐Guzik

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.

arXiv:1711.11240Nov 30, 2017113 citations