Spectral asymmetry of quantum feature maps with real world classical data

Expressing classical data on quantum Hamiltonians for near term quantum machine learning algorithms is expected to provide an advantage over classical algorithms, particularly for quantum kernel methods[1]. Recently, supervised and unsupervised learning demonstrated better accuracy performance using quantum kernels in classification tasks [2]. We evaluate the spectral composition of the data feature maps used to obtain the kernel coefficients with real world data. We find the spectral composition reveals characteristics between differing data types. In the case of binary classification, we find spectral asymmetry in the feature space which we can use to classify incoming data. Our results imply that real world classical data is expressed in different symmetry sectors of the Hilbert space. This results in a semi-supervised quantum learning task for binary classification where only one label is needed to estimate the label of incoming data which can be cast with quantum algorithm subroutines. We further find statistically significant ground state overlap for ZZ feature maps between data classes and establish performance metrics using overlap probabilities.

[1] Vojtech Havlícek, et. al., Nature 567 209-212 (2019)

[2] Oleksandr Kyriienko and Einar Magnussen, ArXiv 2208.01203 (2022)