Discretizing spacetime is often a natural step towards modelling physical systems. For
quantum systems, if we also demand a strict bound on the speed of information propagation …

This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

We provide the first example of a symmetry protected quantum phase that has universal
computational power. This two-dimensional phase is protected by one-dimensional linelike …

Describing a particle in an external electromagnetic field is a basic task of quantum
mechanics. The standard scheme for this is known as “minimal coupling” and consists of …

We provide a classification of translation invariant one-dimensional quantum walks with
respect to continuous deformations preserving unitarity, locality, translation invariance, a …

Discrete-time quantum walks (DTQWs) provide a convenient platform for a realization of
many topological phases in noninteracting systems. They often offer more possibilities than …

Quantum anomalies lead to finite expectation values that defy the apparent symmetries of a
system. These anomalies are at the heart of topological effects in electronic, photonic, and …

We investigate the symmetries of the so-called generalized extended Cantero–Moral–
Velázquez (CMV) matrices. It is well-documented that problems involving reflection …

We present a quantum algorithm for ranking the nodes of a network in their order of
importance. The algorithm is based on a directed discrete-time quantum walk and works on …

We discuss an efficient physical realization of topological quantum walks on a one-
dimensional finite lattice with periodic boundary conditions (circle). The N-point lattice is …