The CGMV method for quantum walks

Renato Portugal

Norio Konno, Etsuo Segawa

We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle, expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al.

Renato Portugal

Norio Konno, Etsuo Segawa

We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. [1] showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle [2], expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al. [3].

Leonid Evgenevich Fedichkin, Fedor Pavlovich Meshchaninov

Clement Boateng Ampadu

Using the Cantero-Grunbaum-Moral-Velazquez (CGMV) method, we obtain the spectral measure for the quantum walk.