English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In quantum and quantum-inspired machine learning, the very first step is toembed the data in quantum space known as Hilbert space. Developing quantumkernel function (QKF), which defines the distances among the samples in theHilbert space, belongs to the fundamental topics for machine learning. In thiswork, we propose the rescaled logarithmic fidelity (RLF) and non-parametricsemi-supervised learning in the quantum space, which we name as RLF-NSSL. Therescaling takes advantage of the non-linearity of the kernel to tune the mutualdistances of samples in the Hilbert space, and meanwhile avoids theexponentially-small fidelities between quantum many-qubit states. Beingnon-parametric excludes the possible effects from the variational parameters,and evidently demonstrates the advantages from the space itself. We compareRLF-NSSL with several well-known non-parametric algorithms including naiveBayes classifiers, k-nearest neighbors, and spectral clustering. Our methodexhibits better accuracy particularly for the unsupervised case with no labeledsamples and the few-shot cases with small numbers of labeled samples. With thevisualizations by t-stochastic neighbor embedding, our results imply that themachine learning in the Hilbert space complies with the principles of maximalcoding rate reduction, where the low-dimensional data exhibit within-classcompressibility, between-class discrimination, and overall diversity. Ourproposals can be applied to other quantum and quantum-inspired machinelearning, including the methods using the parametric models such as tensornetworks, quantum circuits, and quantum neural networks.

Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity