A Low-Complexity Quantum Simulation Framework for Toeplitz-Structured Matrix and Its Application in Signal Processing

Toeplitz matrix reconstruction algorithms (TMRAs) are one of the central subroutines in array processing for wireless communication applications. The classical TMRAs have shown excellent accuracy spectral estimation both uncorrelated and coherence sources recent era. However, incorporate eigenvalue decomposition technique estimating eigenvalues Toeplitz-structured covariance matrices that demand very high computational complexity large arrays. We demonstrate a low-complexity quantum simulation framework exploiting structured Hamiltonian circulant variants. In this framework, we consider two approaches spectrum given matrix: first, an analytical with Jordan form-based sparse-decomposition dense-Toeplitz matrix, second, approximation method conversion into embedding subroutines. also compared efficacy proposed standard phase techniques different time resolutions gate complexities. show gate-complexity analysis our algorithms. Considering dimensions employed random theory deriving error bounds estimated eigenvalues. numerical results obtained partly computer IBM simulator.