Do quantum circuit Born machines generalize?
Do quantum circuit Born machines generalize?
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DOI：
10.1088/2058-9565/acd578
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发表时间：
2023-07-01
影响因子：
6.7
通讯作者：
Perdomo-Ortiz, Alejandro
中科院分区：
文献类型：
--
作者：
Gili, Kaitlin;Hibat-Allah, Mohamed;Perdomo-Ortiz, Alejandro
在最近提出的用于生成任务的量子电路模型中，关于其性能的讨论仅限于其再现已知目标分布的能力。例如，表达模型家族，如量子电路玻恩机（QCBM），几乎完全是根据它们以高精度学习给定目标分布的能力进行评估的。虽然这方面对于某些任务可能是理想的，但它将生成模型的评估范围限制在其记忆数据而不是概括的能力上。因此，人们对模型的泛化性能以及这种能力与资源需求（例如电路深度和训练数据量）之间的关系了解甚少。在这项工作中，我们利用最近提出的泛化评价框架，开始解决这个知识差距。我们首先研究了基数约束分布的QCBM学习过程，并在增加电路深度的同时看到泛化性能的增加。在这里给出的12量子位的例子中，我们观察到训练集中只有30%的有效数据，QCBM在生成看不见的有效数据方面表现出最佳的泛化性能。最后，我们评估的QCBM的能力，不仅推广到有效的样本，但高质量的位串分布根据一个充分的重新加权分布。我们看到，QCBM能够有效地学习重新加权的数据集，并生成比训练集中质量更高的未知样本。据我们所知，这是文献中的第一项工作，它将QCBM的泛化性能作为量子生成模型的整体评估指标，并展示了QCBM泛化到高质量，所需的新样本的能力。
In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as quantum circuit Born machines (QCBMs) have been almost entirely evaluated on their capability to learn a given target distribution with high accuracy. While this aspect may be ideal for some tasks, it limits the scope of a generative model's assessment to its ability to memorize data rather than generalize. As a result, there has been little understanding of a model's generalization performance and the relation between such capability and the resource requirements, e.g. the circuit depth and the amount of training data. In this work, we leverage upon a recently proposed generalization evaluation framework to begin addressing this knowledge gap. We first investigate the QCBM's learning process of a cardinality-constrained distribution and see an increase in generalization performance while increasing the circuit depth. In the 12-qubit example presented here, we observe that with as few as 30% of the valid data in the training set, the QCBM exhibits the best generalization performance toward generating unseen and valid data. Lastly, we assess the QCBM's ability to generalize not only to valid samples, but to high-quality bitstrings distributed according to an adequately re-weighted distribution. We see that the QCBM is able to effectively learn the reweighted dataset and generate unseen samples with higher quality than those in the training set. To the best of our knowledge, this is the first work in the literature that presents the QCBM's generalization performance as an integral evaluation metric for quantum generative models, and demonstrates the QCBM's ability to generalize to high-quality, desired novel samples.