  We compute the complexity for the mixed state density operator derived from a
one-dimensional discrete-time quantum walk (DTQW). The complexity is computed
using a two-qubit quantum circuit obtained from canonically purifying the mixed
state. We demonstrate that the Nielson complexity for the unitary evolution
oscillates around a mean circuit depth of $k$. Further, the complexity of the
step-wise evolution operator grows cumulatively and linearly with the steps.
From a quantum circuit perspective, this implies a succession of circuits of
(near) constant depth to be applied to reach the final state.
