Introducing nonlinear activations into quantum generative models
Introducing nonlinear activations into quantum generative models
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DOI：
10.1103/physreva.107.012406
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发表时间：
2022-05
影响因子：
2.9
通讯作者：
Kaitlin Gili;Mykolas Sveistrys;C. Ballance
中科院分区：
文献类型：
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作者：
Kaitlin Gili;Mykolas Sveistrys;C. Ballance
由于量子力学的线性，设计将非线性激活嵌入状态向量演化的量子生成机器学习模型仍然是一个挑战。然而，一些最成功的经典生成模型，例如基于神经网络的模型，涉及用于质量训练的高度非线性动态。在本文中，我们通过引入一个模型来探索这些动力学在量子生成建模中的作用，该模型通过神经网络结构将非线性激活添加到标准Born Machine框架-量子神经元Born Machine（QNBM）。为了实现这一点，我们利用以前介绍的量子神经元子程序，这是一个重复，直到成功的电路与中间电路测量和经典控制。在介绍QNBM之后，我们通过训练具有4个输出神经元和各种输入和隐藏层大小的3层QNBM来研究其性能如何取决于网络大小。然后，我们比较我们的非线性QNBM的线性量子电路玻恩机（QCBM）。我们为每个模型分配类似的时间和内存资源，因此唯一的主要区别是QNBM所需的量子位开销。通过基于梯度的训练，我们表明，虽然两种模型都可以轻松地学习一个平凡的均匀概率分布，但在更具挑战性的一类分布上，QNBM的错误率比具有类似数量的可调参数的QCBM小近3倍。因此，我们提供的证据表明，非线性是一个有用的资源，在量子生成模型，我们提出了QNBM作为一个新的模型，具有良好的生成性能和潜在的量子优势。
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.