We discuss an efficient physical realization of topological quantum walks on a finite lattice. The N-point lattice is realized with log2N 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.
@article{arxiv.1710.03615,
title = {Physical realization of topological quantum walks on IBM-Q and beyond},
author = {Radhakrishnan Balu and Daniel Castillo and George Siopsis},
journal= {arXiv preprint arXiv:1710.03615},
year = {2017}
}