The recently proposed Quantum Neuron Born Machine (QNBM) has demonstrated quality initial performance as the first quantum generative machine learning (ML) model proposed with non-linear activations. However, previous investigations have been limited in scope with regards to the model's learnability and simulatability. In this work, we make a considerable leap forward by providing an extensive deep dive into the QNBM's potential as a generative model. We first demonstrate that the QNBM's network representation makes it non-trivial to be classically efficiently simulated. Following this result, we showcase the model's ability to learn (express and train on) a wider set of probability distributions, and benchmark the performance against a classical Restricted Boltzmann Machine (RBM). The QNBM is able to outperform this classical model on all distributions, even for the most optimally trained RBM among our simulations. Specifically, the QNBM outperforms the RBM with an improvement factor of 75.3x, 6.4x, and 3.5x for the discrete Gaussian, cardinality-constrained, and Bars and Stripes distributions respectively. Lastly, we conduct an initial investigation into the model's generalization capabilities and use a KL test to show that the model is able to approximate the ground truth probability distribution more closely than the training distribution when given access to a limited amount of data. Overall, we put forth a stronger case in support of using the QNBM for larger-scale generative tasks.

翻译：最近提出的量子神经元玻恩机（QNBM）作为首个引入非线性激活函数的量子生成机器学习（ML）模型，已展现出初步的优异性能。然而，先前关于该模型可学习性与可模拟性的研究范围有限。在本工作中，我们通过深入剖析QNBM作为生成模型的潜力实现了重大突破。首先，我们证明QNBM的网络表征使其难以被经典计算高效模拟。基于此结果，我们展示了该模型学习（表达和训练）更广泛概率分布的能力，并将其性能与经典受限玻尔兹曼机（RBM）进行基准测试。在所有分布上，QNBM均优于该经典模型，即便与模拟中训练最优的RBM相比也是如此。具体而言，对于离散高斯分布、基数约束分布以及Bars and Stripes分布，QNBM分别以75.3倍、6.4倍和3.5倍的性能提升超越RBM。最后，我们初步探究了模型的泛化能力，并利用KL检验表明，在有限数据条件下，该模型能比训练分布更逼近真实概率分布。总体而言，我们为支持将QNBM应用于更大规模生成任务提供了更有力的论证。