Sparse matrices Archives - IEEE Transactions on Quantum Engineering

A Proposed Quantum Framework for Low-Complexity Quantum Simulation and Spectrum Estimation of Hankel-Patterned Systems

The structured matrix completion problem (SMCP) is ubiquitous in several signal processing applications. In this article, we consider a fixed pattern, namely, the Hankel-structure for the SMCP under quantum formalism. By exploiting its structure, a lower-gate-complexity quantum circuit realization of a Hankel system is demonstrated. Further, we propose a quantum simulation algorithm for the Hankel-structured […]

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

June 14, 2023Mostafizur Rahaman LaskarEnabling TechnologiesComputational modeling, Covariance matrices, Eigenvalues and eigenfunctions, Estimation, Quantum computing, Quantum state, Sparse matrices

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 in the spectral estimation for both uncorrelated and coherence sources in the recent era. However, TMRAs incorporate the classical eigenvalue decomposition technique for estimating the eigenvalues of the Toeplitz-structured covariance […]