Measurement-based quantum phase estimation algorithm for finding eigenvalues of non-unitary matrices
Hefeng Wang, Lian-Ao Wu, Yu-xi Liu, Franco Nori · Physical Review A · 2010
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues and eigenvectors. This proposal combines ideas of frequent measurement, measured quantum Fourier transform, and quantum state tomography. It provides a generalization of the conventional phase estimation algorithm, which is limited to Hermitian or unitary matrices.