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International Joint Conference on Neural Networks (IJCNN)

A Study on Learning with a Quantum Neural Network

M. Kinjo, Shigeo Sato, Kiyotaka Nakajima

Published Jan 1, 2006• 5 citations
Publisher

Abstract

A quantum neural network based on the adiabatic quantum computation is one of candidates to overcome the difficulty for developing a quantum computation algorithm. In this paper, we propose a new learning method for a quantum neural network inspired by Hebb learning. Preliminary but successful results by numerical simulations have been shown. The results indicate that a quantum learning like Hebb rule can be implemented.

DOI
10.1109/ijcnn.2006.1716091

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A quantum neural network based on the adiabatic quantum computation is one of candidates to overcome the difficulty for developing a quantum computation algorithm. In this paper, we propose a new learning method for a quantum neural network inspired by Hebb learning. Preliminary but successful results by numerical simulations have been shown. The results indicate that a quantum learning like Hebb rule can be implemented.
Utilizing the enormous potential of quantum computers requires new and practical quantum algorithms. Motivated by the success of machine learning, we investigate the fusion of neural and quantum computing, and propose a learning method for a quantum neural network inspired by the Hebb rule. Based on an analogy between neuron-neuron interactions and qubit-qubit interactions, the proposed quantum learning rule successfully changes the coupling strengths between qubits according to training data. To evaluate the effectiveness and practical use of the method, we apply it to the memorization process of a neuro-inspired quantum associative memory model. Our numerical simulation results indicate that the proposed quantum versions of the Hebb and anti-Hebb rules improve the learning performance. Furthermore, we confirm that the probability of retrieving a target pattern from multiple learned patterns is sufficiently high.
The advantage of quantum mechanical dynamics in information processing has attracted much interest, and dedicated studies on quantum computation algorithms indicate that a quantum computer has remarkable computational power in certain tasks. Quantum properties such as quantum superposition and quantum tunneling are worth studying because they may overcome the weakness of gradient descent method in classical neural networks. Also, the technique established for neural networks can be useful for developing a quantum algorithm. In this chapter, first the authors show the effectiveness of incorporating quantum dynamics and then propose neuromorphic adiabatic quantum computation algorithm based on the adiabatic change of Hamiltonian. The proposed method can be viewed as one of complex-valued neural networks because a qubit operates like a neuron. Next, the performance of the proposed algorithm is studied by applying it to a combinatorial optimization problem. Finally, they discuss the learning ability and hardware implementation.
The advantage of quantum mechanical dynamics in information processing has attracted much interest, and dedicated studies on quantum computation algorithms indicate that a quantum computer has remarkable computational power in certain tasks. Quantum properties such as quantum superposition and quantum tunneling are worth studying because they may overcome the weakness of gradient descent method in classical neural networks. Also, the technique established for neural networks can be useful for developing a quantum algorithm. In this chapter, first the authors show the effectiveness of incorporating quantum dynamics and then propose neuromorphic adiabatic quantum computation algorithm based on the adiabatic change of Hamiltonian. The proposed method can be viewed as one of complex-valued neural networks because a qubit operates like a neuron. Next, the performance of the proposed algorithm is studied by applying it to a combinatorial optimization problem. Finally, they discuss the learning ability and hardware implementation.Request access from your librarian to read this chapter's full text.
This paper proposes a novel architecture for quantum neural networks (QNNs) inspired by biological neural networks, specifically focusing on adaptive learning capabilities. The core idea is to integrate biological mechanisms such as synaptic plasticity and long-range dependencies into the quantum learning process. The traditional approach to QNN training often relies on gradient-based methods, which can be inefficient and susceptible to local minima. This work introduces a bio-inspired approach that leverages the inherent parallelism and quantum superposition of QNNs to achieve more robust and adaptive learning. We formulate the learning process using a modified Hebbian learning rule combined with a quantum measurement process. The key innovation lies in dynamically adjusting the quantum gates based on the network's internal state, mimicking the neural network's ability to adapt to changing environments. The resulting QNN architecture exhibits enhanced learning speed and improved generalization performance compared to conventional QNNs. The theoretical framework is presented, and the underlying mathematical equations are detailed, providing a robust foundation for further research and development in this field.
There is increasing interest in quantum computing, because of its enormous computing potential. A small number of powerful quantum algorithms have been proposed to date; however, the development of new quantum algorithms for practical use remains essential. Parallel computing with a neural network has successfully realized certain unique functions such as learning and recognition; therefore, the introduction of certain neural computing techniques into quantum computing to enlarge the quantum computing application field is worthwhile. In this paper, a novel quantum associative memory (QuAM) is proposed, which is achieved with a quantum neural network by employing adiabatic Hamiltonian evolution. The memorization and retrieval procedures are inspired by the concept of associative memory realized with an artificial neural network. To study the detailed dynamics of our QuAM, we examine two types of Hamiltonians for pattern memorization. The first is a Hamiltonian having diagonal elements, which is known as an Ising Hamiltonian and which is similar to the cost function of a Hopfield network. The second is a Hamiltonian having non-diagonal elements, which is known as a neuro-inspired Hamiltonian and which is based on interactions between qubits. Numerical simulations indicate that the proposed methods for pattern memorization and retrieval work well with both types of Hamiltonians. Further, both Hamiltonians yield almost identical performance, although their retrieval properties differ. The QuAM exhibits new and unique features, such as a large memory capacity, which differs from a conventional neural associative memory.