  The quantum walk formalism is a widely used and highly successful framework
for modeling quantum systems, such as simulations of the Dirac equation,
different dynamics in both the low and high energy regime, and for developing a
wide range of quantum algorithms. Here we present the circuit-based
implementation of a discrete-time quantum walk in position space on a
five-qubit trapped-ion quantum processor. We encode the space of walker
positions in particular multi-qubit states and program the system to operate
with different quantum walk parameters, experimentally realizing a Dirac
cellular automaton with tunable mass parameter. The quantum walk circuits and
position state mapping scale favorably to a larger model and physical systems,
allowing the implementation of any algorithm based on discrete-time quantum
walks algorithm and the dynamics associated with the discretized version of the
Dirac equation.
