Quantum Fisher kernel for mitigating the vanishing similarity issue
Quantum Fisher kernel for mitigating the vanishing similarity issue
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DOI：
10.1088/2058-9565/ad4b97
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发表时间：
2022-10
影响因子：
6.7
通讯作者：
Yudai Suzuki;Hideaki Kawaguchi;Naoki Yamamoto
中科院分区：
文献类型：
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作者：
Yudai Suzuki;Hideaki Kawaguchi;Naoki Yamamoto
量子内核（QK）方法利用量子计算机来计算QK用于使用基于内核的学习模型。尽管该方法具有潜在的量子优势，但常用的基于忠诚度的QK遇到了有害问题，我们称之为消失的相似性问题。期望值的指数衰减和QK的差异会随着量子数的增加而降低模型的可行性和训练性。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，当使用浅层交替分层ansatzes时，QFK可以避免问题。此外，傅立叶分析在数值上阐明了QFK可以具有与基于Fidelity的QK相当的表达性。此外，我们演示了合成分类任务，其中QFK由于没有消失的相似性而优于基于保真度的QK。这些结果表明，QFK为量子机学习的实际应用铺平了道路。
Quantum kernel (QK) methods exploit quantum computers to calculate QKs for the use of kernel-based learning models. Despite a potential quantum advantage of the method, the commonly used fidelity-based QK suffers from a detrimental issue, which we call the vanishing similarity issue; the exponential decay of the expectation value and the variance of the QK deteriorates implementation feasibility and trainability of the model with the increase of the number of qubits. 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 can avoid the issue when shallow alternating layered ansatzes are used. In addition, the Fourier analysis numerically elucidates that the QFK can have the expressivity comparable to the fidelity-based QK. Moreover, we demonstrate synthetic classification tasks where QFK outperforms the fidelity-based QK in performance due to the absence of vanishing similarity. These results indicate that QFK paves the way for practical applications of quantum machine learning toward possible quantum advantages.