Introducing Non-Linear Activations into Quantum Generative Models

TL;DR

This paper introduces a novel quantum generative model called the Quantum Neuron Born Machine (QNBM) that incorporates non-linear activations, demonstrating improved performance over traditional linear quantum models in learning complex distributions.

Contribution

The paper presents the QNBM, a new quantum generative model embedding non-linear activations via neural network structures, showing enhanced learning capabilities compared to linear models.

Findings

QNBM achieves nearly 3x smaller error than QCBM on complex distributions.

Non-linearity improves quantum generative model performance.

QNBM demonstrates potential for quantum advantage in generative tasks.

Abstract

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. In this paper, 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). To achieve this, we utilize a previously introduced Quantum Neuron subroutine, which is a repeat-until-success circuit with mid-circuit measurements and classical control. After introducing the QNBM, we investigate how its performance depends on network size, by training a 3-layer QNBM with 4 output neurons and various input and hidden layer sizes. We then compare our non-linear QNBM to the linear Quantum Circuit Born Machine (QCBM). We allocate similar time and memory resources to each model, such that the only major difference is the qubit overhead required by the QNBM. With gradient-based training, we show that while both models can easily learn a trivial uniform probability distribution, on a more challenging class of distributions, the QNBM achieves an almost 3x smaller error rate than a QCBM with a similar number of tunable parameters. 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.