Neuro-inspired Quantum Learning Rule Inspired by Boltzmann Machine*

To introduce learning function into quantum computing, we have investigated the method to operate a quantum neural network (QNN) in the similar manner for a classical neural network. Thanks to the analogy between neuron-neuron and qubit-qubit interactions [S. Sato et al., 2003, and M. Kinjo et al., 2005], we have established a new model of quantum associative memory (QuAM) [Y. Osakabe et al., 2017]. It means that we have proposed a method for a QNN to store multiple target patterns with a Hamiltonian, but an iterative learning scheme was not developed at that time. Thus, this paper proposes a quantum learning method for a QNN inspired by Hebbian and anti-Hebbian learning utilized in Boltzmann machine (BM); the quantum versions of Hebb and anti-Hebb rules of BM are developed by tuning coupling strengths among qubits repeatedly according to probability distribution of a QNN. Numerical results indicate that the proposed quantum learning rules work well and it is confirmed that the combination of quantum Hebb and anti-Hebb rules certainly improves the learning performance of a QNN.