评估经典,量子和混合量子神经网络在解决微分方程中的性能
Navid Markazi1, Behrouz Mirza2
1Department of Physics, Isfahan University of Technology, Isfahan, 84156-83111, Iran. n.markazi@alumni.iut.ac.ir.
Scientific reports
|November 10, 2025
概括
经典,量子和混合量子神经网络在解决微分方程方面进行了比较. 混合量子神经网络经常显示出更高的准确性,而量子神经网络在特定问题上表现出色,需要更少的参数和更快的融合.
科学领域:
- 计算物理 计算物理
- 量子计算是一种量子计算.
- 机器学习 机器学习
背景情况:
- 部分微分方程 (PDEs) 是科学和工程学的基础.
- 经典的神经网络 (NN) 在解决PDEs方面表现有前途.
- 量子计算在计算速度和容量方面提供了潜在的优势.
研究的目的:
- 为了比较经典,量子和混合量子神经网络 (HQNN) 在解决 PDE 的性能.
- 通过监督和无监督学习方法来评估这些网络.
- 在各种物理问题上评估网络性能,包括减弱波器,爱因斯坦场方程和时间独立的施罗丁格方程.
主要方法:
- 用物理信息监督的NN用于调波器和爱因斯坦场方程.
- 基于射击方法的无监督NN算法被开发为时间独立的施罗丁格方程.
- 为HQNN引入了三个变量参数化量子特征图和两个量子电路.
- 网络被测试在三个配置跨多个随机种子.
主要成果:
- 在大多数情况下,在有利的参数初始化条件下,HQNN比经典的NNN取得了更高的准确性.
- 量子神经网络 (QNN) 证明了对减弱波器的最佳准确性,并且在施罗丁格方程上表现良好.
- 无论QNN还是HQNN都需要更少的参数,并且比经典的NNN更快地趋同.
- 所有模型都对参数初始化表现出敏感性,QNN表现出最高的变化.
结论:
- 与古典方法相比,量子和混合量子方法在解决PDE方面提供了与传统方法相比具有竞争力或更高的性能.
- 量子和混合模型的效率和准确性表明它们在推进科学计算方面的潜力.
- 对参数优化和初始化的进一步研究对于最大化量子神经网络的好处至关重要.
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