Learning Rule for a Quantum Neural Network Inspired by Hebbian Learning

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.