变分量子电路中的子空间可控性：利用动力学李代数最大化表达性并提高搜索效率
Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras
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中文总结 AI 辅助
该研究通过MNIST-1D多分类任务验证，子空间可控的变分量子电路在超参数搜索中更易达到最低损失，可限制搜索范围以降低计算成本。
中文摘要 AI 辅助
变分混合量子模型是在量子硬件上实现机器学习的常见范式。然而，由于变分量子电路形成的损失景观固有的若干问题，它们难以训练。为缓解这些问题，研究人员扩展了子空间可控性的概念，从而提高了变分模型在基于量子的任务中找到全局最小值的成功率。然而，尚不清楚这些结果是否扩展到基于经典的任务，以及相对于超参数搜索是否能实现任何优势。我们通过使用可控电路在MNIST-1D上进行多分类任务来开始解决这个问题。我们的结果表明，在超参数搜索中，大多数达到最低训练和验证损失的量子模型是子空间可控的。这些结果表明，超参数搜索可以限制在这样的模型上，从而降低计算成本和时间。
英文摘要
Variational hybrid quantum models are a common paradigm for realising machine learning on quantum hardware. Nonetheless, they are challenging to train due to several problems intrinsic to the loss landscapes formed by variational quantum circuits. To mitigate these issues, researchers have extended the idea of subspace controllability leading to an increase in the success rate of variational models in finding the global minimum for quantum-based tasks. However, it remains unknown whether these results extend to classical-based tasks, and if any advantages are realised over a hyperparameter search. We begin to address this question by employing controllable circuits in a multi- classification task using MNIST-1D. Our results show that over a hyperparameter search, the majority of quantum models that achieve the lowest training and validation losses are subspace controllable. These results indicate that the hyperparameter search can be restricted to such models, in turn reducing computational cost and time.
发表机构
- Deutsches Zentrum für Luft- und Raumfahrt（德国航空航天中心）
- Zentrum für Astronomie der Universität Heidelberg（海德堡大学天文中心）
机构由 AI 辅助整理，请以论文原文为准。
