Quantum algorithm for multiple signal classification

The direction of arrival (DOA) estimation in array signal processing is an important research area. The effectiveness of the direction of arrival greatly determines the performance of multi-input multi-output (MIMO) antennas. The multiple signal classification (MUSIC) algorithm, which is the most canonical and widely used subspace-based method for direction angle estimation, has a moderate estimation performance of DOA. In this article, we present a quantum algorithm for performing MUSIC. Compared with the best-known classical algorithm, quantum MUSIC can show a polynomial speedup. In our scheme, we first efficiently implement a non-Hermitian chain product subroutine for the matrix ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{ss}\ensuremath{\in}{R}^{N\ifmmode\times\else\texttimes\fi{}N}$ with $L$ snapshots, where the method is different from that of Cong and Duan [I. Cong and L. Duan, New J. Phys. 18, 073011 (2016)]. In this subroutine, we perform amplitude transduction [Y. R. Sanders, G. H. Low, A. Scherer, and D. W. Berry, Phys. Rev. Lett. 122, 020502 (2019)] by testing an inequality to neglect the calculation of the approximate arcsine function. Second, a quantum labeling operation based on the principal eigenvalues is proposed for preparing the coherent state of the principal eigenvectors. Finally, we generalize our results to some quantum algorithms with quantum principal component analysis subroutines and some existing quantum algorithms where the covariance matrices occur in the non-Hermitian chain product form.