Akito Suzuki

Generator of an abstract quantum walk

We give an explicit formula of the generator of an abstract Szegedy evolution operator in terms of the discriminant operator of the evolution. We also characterize the asymptotic behavior of a quantum walker through the spectral property of the discriminant operator by using the discrete analog of the RAGE theorem.

Asymptotic velocity of a position-dependent quantum walk

We consider a position-dependent coined quantum walk on

Removal of UV Cutoff for the Nelson Model with Variable Coefficients

\mathbb {Z}

Quantum walks with an anisotropic coin I: spectral theory

Z and assume that the coin operator C(x) satisfies

Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations

\begin{aligned} \Vert C(x) - C_0 \Vert \le c_1|x|^{-1-\epsilon }, \quad x \in \mathbb {Z}\setminus \{0\} \end{aligned}

Localization of a multi-dimensional quantum walk with one defect

‖C(x)-C0‖≤c1|x|-1-ϵ,x∈Z\{0}with positive