126 citations · 447 across the 20 of their papers we have counts for
5 papers · 1 filter
The topological classification of one-dimensional symmetric quantum walks
C. Cedzich, T. Geib, F. A. Grünbaum +4
We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalu…
Bulk-edge correspondence of one-dimensional quantum walks
C. Cedzich, F. A. Grünbaum, C. Stahl +3
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 which…
A limit theorem for a 3-period time-dependent quantum walk
F. Alberto Grünbaum, Takuya Machida
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position…
Birth and death processes and quantum spin chains
Alberto F. Grünbaum, Luc Vinet, Alexei Zhedanov
This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that…
Recurrence for discrete time unitary evolutions
F. A. Grünbaum, L. Velázquez, A. H. Werner +1
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 whe…