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

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

2009-06-14

arxiv.org/abs/0906.2538v2

Phys. Rev. A, 82, 062303 (2010)

Physics

Quantum Physics

7 pages, 4 figures

Scientific paper

10.1103/PhysRevA.82.062303

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.

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