  We discuss an efficient physical realization of topological quantum walks on
a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and
the quantum circuit utilizes a number of quantum gates which is polynomial in
the number of qubits. In a certain scaling limit, we show that a large number
of steps is implemented with a number of quantum gates which is independent of
the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit
quantum computer, thus experimentally demonstrating topological features, such
as boundary bound states, on a lattice with $N=4$ points.
