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.

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.