Quantum Kernel Extreme Learning Machine with Multivariate Gaussian Document Representation for Multi-label Soft Classification
TL;DR
Theoretical analysis demonstrates that, in general scenarios, the proposed quantum approach achieves exponential acceleration with respect to the number of document samples $D$ and their cardinality $N$ along with quadratic speedup regarding the dimensionality of sample documents, yielding an overall complexity of O.
Abstract
To address the efficiency bottlenecks inherent in multi-label document learning, this paper proposes a quantum kernel extreme learning machine framework integrated with multivariate Gaussian document representation for efficient multi-label soft classification. The proposed approach leverages quantum computing paradigms to accelerate critical computational steps involved in kernel construction and model training. The proposed approach comprises four key quantum algorithmic components: (i) quantum algorithms for estimating mean vectors and empirical covariance matrices under multivariate Gaussian distribution; (ii) quantum subroutines for computing their corresponding Euclidean and Frobenius norms; (iii) a quantum procedure for constructing the density operator associated with the kernel matrix via partial trace; and (iv) a complete quantum kernel extreme learning machine architecture for probabilistic multi-label document prediction. Theoretical analysis demonstrates that, in general scenarios, the proposed quantum approach achieves exponential acceleration with respect to the number of document samples $D$ and their cardinality $N$, along with quadratic speedup regarding the dimensionality $M$ of sample documents, yielding an overall complexity of $\mathcal{O}\left(M\text{poly}\log\left(DMN\right)\right)$ compared to the classical $\mathcal{O}\left(DNM^2+D^2M^2+D^3\right)$, under standard assumptions regarding condition numbers and error parameters.