Quantum walks, the quantum mechanical counterpart of classical random walks, is an
advanced tool for building quantum algorithms that has been recently shown to constitute a …

We study the spectral analysis and the scattering theory for time evolution operators of
position-dependent quantum walks. Our main purpose of this paper is the construction of …

We consider quantum dynamical systems specified by a unitary operator U and an initial
state vector ϕ. In each step the unitary is followed by a projective measurement checking …

We outline a theory of symmetry protected topological phases of one-dimensional quantum
walks. We assume spectral gaps around the symmetry-distinguished points+ 1 and− 1, in …

We consider a position-dependent coined quantum walk on ZZ and assume that the coin
operator C (x) satisfies ‖ C (x)-C_0 ‖ ≤ c_1| x|^-1-ϵ,\quad x ∈ Z ∖ {0\}‖ C (x)-C 0‖≤ c …

We treat three types of measures of the quantum walk (QW) with the spatial perturbation at
the origin, which was introduced by Konno (Quantum Inf Proc 9: 405, 2010): time averaged …

A notion of monitored recurrence for discrete-time quantum processes was recently
introduced in Grünbaum et al.(Commun Math Phys (2), 320: 543–569, 2013) taking the …

We review the main aspects of a recent approach to quantum walks, the CGMV method. This
method proceeds by reducing the unitary evolution to canonical form, given by the so-called …

We consider ad-dimensional random quantum walk with site-dependent random coin
operators. The corresponding transition coefficients are characterized by deterministic …

We perform the spectral analysis of the evolution operator U of quantum walks with an
anisotropic coin, which include one-defect models, two-phase quantum walks, and …