Quantum Speedup for Spectral Approximation of Kronecker Products

Given its widespread application in machine learning and optimization, the Kronecker product emerges as a pivotal linear algebra operator. However, its computational demands render it an expensive operation, leading to heightened costs in spectral approximation of it through traditional computation algorithms. Existing classical methods for spectral approximation exhibit a linear dependency on the matrix dimension denoted by $n$, considering matrices of size $A_1 \in \mathbb{R}^{n \times d}$ and $A_2 \in \mathbb{R}^{n \times d}$. Our work introduces an innovative approach to …

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