Leadbeater Chiara, Sharrock Louis, Coyle Brian, Benedetti Marcello
Cambridge Quantum Computing Limited, London SW1E 6DR, UK.
Department of Mathematics, Imperial College London, London SW7 2AZ, UK.
Entropy (Basel). 2021 Sep 30;23(10):1281. doi: 10.3390/e23101281.
Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit born machine. In particular, we consider training a quantum circuit born machine using -divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any -divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the born machine. The first is based on -divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing -divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback-Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another -divergence, namely, the Pearson divergence.
生成建模是机器学习中一项重要的无监督任务。在这项工作中，我们研究了一种基于量子电路生成机的混合量子 - 经典方法来处理此任务。具体而言，我们考虑使用散度来训练量子电路生成机。我们首先讨论生成建模的对抗框架，该框架能够在近期估计任何散度。基于此能力，我们引入了两种启发式方法，它们显著改进了生成机的训练。第一种基于训练期间的散度切换。第二种将局部性引入散度，在类似应用中，就缓解贫瘠高原而言，这一策略已被证明很重要。最后，我们讨论量子设备对计算散度的长期影响，包括为散度估计提供二次加速的算法。特别是，我们推广了用于估计库尔贝克 - 莱布勒散度和总变差距离的现有算法，以获得一种用于估计另一种散度（即皮尔逊散度）的容错量子算法。
