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.
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.
It is widely believed that the real parallel computation achieved by quantum computers has an enormous computing potential. In order to expand its applicable field, we have investigated the fusion of quantum and neural computations. As a first step of implementing learning function on quantum computers, we have proposed a novel quantum associative memory (QuAM) by considering an analogy between neural associative network and qubit network. The memorizing procedure of the QuAM is realized with a Hamiltonian derived from qubit-qubit interactions, and the retrieving procedure is based on the adiabatic Hamiltonian evolution. The memory capacity of the QuAM has been nominally estimated as 2N-1where N is a number of qubits, but its retrieve property has not been discussed in our previous study. This paper proposes a retrieving process for the QuAM and evaluates its performance in detail. The results indicate that the average of the retrieving probability is over 50% even when the qubit network memorizes 2N-1patterns and thus the QuAM is successfully implemented.
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.
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.
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.
Introduction This study investigates integrating quantum-inspired learning models with traditional Hebbian learning within neural networks, comparing their performance in learning efficiency, generalization, stability, and robustness. Traditional Hebbian models are biologically plausible but often struggle with stability, scalability, and adaptability. In contrast, quantum-inspired models leverage quantum mechanics principles like superposition and entanglement to enhance neural network performance potentially. Methods The simulations were conducted using a neural network comprising 1,000 neurons and 100 patterns across 10 instances. The key parameters included a fixed decay rate of 0.005, 80% excitatory neurons, and 10% fixed connectivity. The study varied learning rates (0.01, 0.05, 0.1) and thresholds (0.3, 0.5, 0.7) to assess different parameter settings. The performance metrics evaluated included accuracy, precision, recall, and F1-Score. Results The results showed that quantum-inspired models achieved significantly higher accuracy and precision, enhancing their reliability in class prediction and reducing false positives. Conversely, Hebbian models excelled in recall and F1-Score, effectively identifying positive cases and balancing precision and recall. Additionally, quantum-inspired models demonstrated greater stability, robustness, and consistent performance across varying parameters. Conclusion Quantum-inspired models offer notable improvements in learning efficiency, generalization, stability, and robustness, while Hebbian models perform better in recall and F1-Score. These findings suggest the potential for hybrid models that combine the strengths of both approaches, aiming for more balanced and efficient learning systems. Future research should explore these hybrid models to enhance performance across diverse artificial intelligence applications. Supplementary materials include the complete R code used, enabling replication and further investigation of the results.