利用量子地球移动器的距离学习量子数据
Learning quantum data with the quantum Earth Mover's distance
摘要：
量化学习算法的输出距离其目标有多远是机器学习中的一项重要任务。然而，在量子环境中，常用的距离度量的损失景观往往会产生不良的结果，如穷人的局部最小值和指数衰减梯度。为了克服这些障碍，我们考虑在这里最近提出的量子地球移动（EM）或Wasserstein-1距离作为一个量子模拟的经典EM距离。我们证明了量子EM距离具有其他常用量子距离度量所没有的独特性质，这使得量子学习更加稳定和有效。我们提出了一个量子Wasserstein生成对抗网络（qWGAN），它利用了量子EM距离，并提供了一种对量子数据进行学习的有效方法。我们提供的例子中，我们的qWGAN是能够学习一组不同的量子数据，只有资源多项式的量子位数。
英文摘要：
Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly used distance metrics often produce undesirable outcomes such as poor local minima and exponentially decaying gradients. To overcome these obstacles, we consider here the recently proposed quantum earth mover's (EM) or Wasserstein-1 distance as a quantum analog to the classical EM distance. We show that the quantum EM distance possesses unique properties, not found in other commonly used quantum distance metrics, that make quantum learning more stable and efficient. We propose a quantum Wasserstein generative adversarial network (qWGAN) which takes advantage of the quantum EM distance and provides an efficient means of performing learning on quantum data. We provide examples where our qWGAN is capable of learning a diverse set of quantum data with only resources polynomial in the number of qubits.
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