论文标题
通过降低编码率的样品效率量子出生的机器
Sample-efficient Quantum Born Machine through Coding Rate Reduction
论文作者
论文摘要
量子电路诞生的机器（QCBM）是一种量子物理启发的隐式生成模型，自然适合学习二进制图像，具有建模离散分布的潜在优势，而离散分布很难经典地模拟。随着数据样本是通过机械机械生成的，QCBM涵盖了独特的优化景观。但是，QCBMS上的开拓性工作不考虑在训练过程中仅允许小批量尺寸的实际情况。在图像空间中经过统计两样本测试目标训练的QCBM需要大量的投影测量，以远近近似模型分布，这是由于概率空间的指数缩放而对大规模量子系统而言是非实践的。 QCBM经过对抗性的QCBM针对深度神经网络歧视者是概念验证模型，面临模式崩溃。在这项工作中，我们研究了QCBM的实践学习。我们将信息理论\ textit {最大编码率降低}（mcr $^2 $）公制作为匹配工具，并研究其对QCBMS模式崩溃的影响。我们计算有或没有明确特征映射的量子电路参数的MCR $^2 $的基于采样的梯度。我们在实验上表明，仅到第二瞬间匹配就不足以训练量子发生器，但是当与类概率估计损失结合使用时，MCR $^2 $能够抵抗模式崩溃。此外，我们表明，具有对抗性训练的神经网络内核进行无限矩匹配也有效地在模式崩溃中。在条纹数据集上，我们提出的技术减轻了比以前的QCBM培训方案更大的程度崩溃的程度，从而迈向了实用性和可扩展性。
The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate classically. As data samples are generated quantum-mechanically, QCBMs encompass a unique optimization landscape. However, pioneering works on QCBMs do not consider the practical scenario where only small batch sizes are allowed during training. QCBMs trained with a statistical two-sample test objective in the image space require large amounts of projective measurements to approximate the model distribution well, unpractical for large-scale quantum systems due to the exponential scaling of the probability space. QCBMs trained adversarially against a deep neural network discriminator are proof-of-concept models that face mode collapse. In this work we investigate practical learning of QCBMs. We use the information-theoretic \textit{Maximal Coding Rate Reduction} (MCR$^2$) metric as a second moment matching tool and study its effect on mode collapse in QCBMs. We compute the sampling based gradient of MCR$^2$ with respect to quantum circuit parameters with or without an explicit feature mapping. We experimentally show that matching up to the second moment alone is not sufficient for training the quantum generator, but when combined with the class probability estimation loss, MCR$^2$ is able to resist mode collapse. In addition, we show that adversarially trained neural network kernel for infinite moment matching is also effective against mode collapse. On the Bars and Stripes dataset, our proposed techniques alleviate mode collapse to a larger degree than previous QCBM training schemes, moving one step closer towards practicality and scalability.
