Quantum data parallelism in quantum neural networks

Quantum neural networks hold promise for achieving lower generalization error bounds and enhanced computational efficiency in processing certain datasets. However, the integration of quantum superposition in data parallelism—a key aspect in the applications of classical neural network—has been largely unexplored in the context of quantum neural networks. Here, we demonstrate the effective application of quantum parallelism, via quantum superposition and entanglement, to achieve data parallelism in generic quantum neural network models. We address two classes of encoding schemes for the training data: as orthogonal and nonorthogonal quantum states, respectively. With orthogonal encoding, we rigorously prove that parallel and individual training are equivalent in terms of the loss function, a result directly derived from quantum entanglement; with nonorthogonal encoding, we show that parallel computing remains viable, and quantum interference among data becomes notable. We perform a comparative numerical analysis in these different scenarios, exploring various quantum neural networks with or without superposed data input, highlighting the validity of quantum data parallelism.