Representation Learning via Quantum Neural Tangent Kernels
Representation Learning via Quantum Neural Tangent Kernels
复制标题
通过量子神经正切核进行表示学习
DOI：
10.1103/prxquantum.3.030323
复制
发表时间：
2022
期刊：
影响因子：
9.7
通讯作者：
Mezzacapo, Antonio
中科院分区：
文献类型：
--
作者：
Liu, Junyu;Tacchino, Francesco;Glick, Jennifer R.;Jiang, Liang;Mezzacapo, Antonio
变分量子电路用于量子机器学习和变分量子模拟任务。设计良好的变分电路或预测它们在给定的学习或优化任务中的表现仍然不清楚。在这里，我们讨论这些问题，分析变分量子电路使用神经正切核理论。我们定义了量子神经正切核，并推导出优化和学习任务中相关损失函数的动力学方程。我们解析地解决了冻结极限或懒惰训练机制中的动力学，其中变角变化缓慢，线性扰动就足够好了。我们扩展到一个动态的设置，包括二次修正的变角分析。然后，我们考虑一个混合量子经典架构，并定义了一个大宽度限制的混合内核，表明一个混合量子经典神经网络可以近似高斯。这里给出的结果显示了对用于量子机器学习和优化问题的变分量子电路的训练动力学的分析理解是可能的。这些分析结果得到了量子机器学习实验的数值模拟的支持。
Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.
影响因子：
16.6
作者：
Canatar A;Bordelon B;Pehlevan C
通讯作者：
Pehlevan C
影响因子：
6.8
作者：
Halverson, James;Maiti, Anindita;Stoner, Keegan
通讯作者：
Stoner, Keegan