Quantum Speedup for Spectral Approximation of Kronecker Products
Yeqi Gao Zhao Song Ruizhe Zhang
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 efficiently address the
spectral approximation of the Kronecker product $A_1 \otimes A_2$ using quantum
methods. By treating matrices as quantum states, our proposed method
significantly reduces the time complexity of spectral approximation to
$O_{d,\epsilon}(\sqrt{n})$.