The aim of this paper is to build quantum circuits that implement discrete-time quantum
walks having an arbitrary position-dependent coin operator. The position of the walker is …

A single-particle framework for unitary lattice gauge theory in discrete time - IOPscience
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Discrete-time quantum walks (QWs) are transportation models of single quantum particles
over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a …

We classify qubit QCAs on lattices $\mathbb Z^ s $ with von Neumann neighbourhood
scheme, in terms of feasibility as finite depth quantum circuits. We show the most general …

We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices
that consists in grouping neighboring cells into tiles and selecting a subspace within each …

Identical quantum particles exhibit only two types of statistics: bosonic and fermionic.
Theoretically, this restriction is commonly established through the symmetrization postulate …

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of
local fermionic modes that evolve according to one step of the Dirac cellular automaton …

We present a fermionic cellular automaton model which describes massless Dirac fermions
in 1+ 1 dimension coupled with local, number preserving interaction. The diagonalization of …

We consider introducing the Dirac sea in a discrete spacetime model of fermions which
approximates the Dirac equation in the continuum limit. However, if we attempt to fill up …

Discrete-time quantum walks with position-dependent coin operators have numerous
applications. For a position dependence that is sufficiently smooth, it has been provided in …