论文标题
量子Fisher内核缓解消失的相似性问题
Quantum Fisher kernel for mitigating the vanishing similarity issue
论文作者
论文摘要
量子内核方法是一种机器学习模型，利用量子计算机来计算测量数据之间相似性的量子内核（QK）。尽管该方法具有潜在的量子优势，但通常使用的基于保真度的QK遇到了有害问题，我们称之为消失的相似性问题。由于QK期望的指数下降和差异，检测数据之间的差异会随着量子数数量的增加而变得困难。这意味着需要设计基于保真度的QK替代方案。在这项工作中，我们提出了一个新的QK类，称为量子Fisher内核（QFK），这些QK考虑了数据源的几何结构。我们通过分析和数值证明，当使用交替的分层ANSATZS（ALAS）时，基于反对称对数衍生物（ALDQFK）的QFK可以避免问题，而基于fidelity的QK则甚至无法与Alas一起使用。此外，傅立叶分析在数值上阐明了ALDQFK可以具有与基于Fidelity的QK相当的表达性。这些结果表明，QFK为具有量子优势的量子机学习的实际应用铺平了道路。
Quantum kernel method is a machine learning model exploiting quantum computers to calculate the quantum kernels (QKs) that measure the similarity between data. Despite the potential quantum advantage of the method, the commonly used fidelity-based QK suffers from a detrimental issue, which we call the vanishing similarity issue; detecting the difference between data becomes hard with the increase of the number of qubits, due to the exponential decrease of the expectation and the variance of the QK. This implies the need to design QKs alternative to the fidelity-based one. In this work, we propose a new class of QKs called the quantum Fisher kernels (QFKs) that take into account the geometric structure of the data source. We analytically and numerically demonstrate that the QFK based on the anti-symmetric logarithmic derivatives (ALDQFK) can avoid the issue when the alternating layered ansatzs (ALAs) are used, while the fidelity-based QK cannot even with the ALAs. Moreover, the Fourier analysis numerically elucidates that the ALDQFK can have expressivity comparable to that of the fidelity-based QK. These results indicate that the QFK paves the way for practical applications of quantum machine learning with possible quantum advantages.
