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

Physical realization of topological quantum walks on IBM-Q and beyond