Generative Modeling with Quantum Neurons

Due to the linearity of quantum mechanics, it remains a challenge to design quantum

generative machine learning models that embed non-linear activations into the evolution of the

statevector. However, some of the most successful classical generative models, such as those

based on neural networks, involve highly non-linear dynamics for quality training. Here, we

explore the effect of these dynamics in quantum generative modeling by introducing a model that

adds non-linear activations via a neural network structure onto the standard Born Machine

framework - the Quantum Neuron Born Machine (QNBM). Further, we investigate the QNBM’s

performance relative to network size, and demonstrate that it performs best without a hidden

layer. We then compare the QNBM to the classical Restricted Boltzmann Machine (RBM) on a

wide range of probability distributions, and see that the QNBM is able to outperform this model

consistently. Lastly, we compare the QNBM to the state-of-the-art Quantum Circuit Born Machine

(QCBM), and demonstrate that it achieves a 3x smaller error rate. We therefore provide evidence

that suggests that non-linearity is a useful resource in quantum generative models, and we put

forth the QNBM as a new model with good generative performance and potential for quantum

advantage.