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 A1 ∈ ℝn × d and A2 ∈ ℝn × d. Our work introduces an innovative approach to efficiently address the spectral approximation of the Kronecker product A1 otimes A2 using quantum methods. By treating matrices as quantum states, our proposed method significantly reduces the time complexity of spectral approximation to Od,ε(√n).