Group-Invariant Quantum Machine Learning
Group-Invariant Quantum Machine Learning
复制标题
群不变量子机器学习
DOI：
10.1103/prxquantum.3.030341
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
M. Cerezo
中科院分区：
文献类型：
--
作者：
Martín Larocca;F. Sauvage;Faris M. Sbahi;Guillaume Verdon;Patrick J. Coles;M. Cerezo
量子机器学习(QML)模型的目标是从以量子态编码的数据中学习。最近，有研究表明，具有很少或没有归纳偏差的模型(即，在模型中没有嵌入关于问题的假设)可能存在可训练性和泛化问题，特别是对于较大的问题规模。因此，开发尽可能多地编码有关手头问题的信息的方案是至关重要的。在这项工作中，我们提出了一个简单但强大的框架，其中使用数据中的底层不变性来构建QML模型，该模型通过构建尊重这些对称性。这些所谓的群不变模型产生在与数据集相关联的对称群G的任何元素的作用下保持不变的输出。我们给出了支持G不变模型设计的理论结果，并通过几个典型的QMLClassifi正交任务来举例说明它们的应用，其中包括当G是连续Lie群时以及当G是离散对称群时的情况。值得注意的是，我们的框架允许我们以一种优雅的方式恢复文献中的几个著名算法，以及发现新的算法。综上所述，我们预计我们的结果将有助于为更多的几何和群论方法来设计QML模型铺平道路。
Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group G associated to the dataset. We present theoretical results underpinning the design of G -invariant models, and exemplify their application through several paradigmatic QML classification tasks including cases when G is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.
影响因子：
7.6
作者：
Gard, Bryan T.;Zhu, Linghua;Barnes, Edwin
通讯作者：
Barnes, Edwin
影响因子：
56.9
作者：
Huang, Hsin-Yuan;Broughton, Michael;McClean, Jarrod R.
通讯作者：
McClean, Jarrod R.
影响因子：
56.9
作者：
Huang, Hsin-Yuan;Kueng, Richard;Preskill, John
通讯作者：
Preskill, John