  Quantum walks are a promising framework for developing quantum algorithms and
quantum simulations. They represent an important test case for the application
of quantum computers. Here we present different forms of discrete-time quantum
walks (DTQWs) and show their equivalence for physical realizations. Using an
appropriate digital mapping of the position space on which a walker evolves to
the multiqubit states of a quantum processor, we present different
configurations of quantum circuits for the implementation of DTQWs in
one-dimensional position space. We provide example circuits for a five-qubit
processor and address scalability to higher dimensions as well as larger
quantum processors.
