Measurement-based quantum phase estimation algorithm for finding eigenvalues of non-unitary matrices

TL;DR

This paper introduces a quantum algorithm that extends phase estimation to non-unitary matrices, enabling the extraction of eigenvalues and eigenvectors through innovative measurement techniques.

Contribution

It presents a novel quantum algorithm that generalizes phase estimation to non-Hermitian matrices using measurement-based methods.

Findings

Successfully constructs non-Hermitian matrices via quantum interactions

Demonstrates eigenvalue and eigenvector extraction for non-unitary matrices

Generalizes phase estimation beyond Hermitian and unitary cases

Abstract

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.