Physical realization of topological quantum walks on IBM-Q and beyond
Radhakrishnan Balu, Daniel Castillo, George Siopsis · Quantum Science and Technology · 2018
Abstract We discuss an efficient physical realization of topological quantum walks on a one-dimensional finite lattice with periodic boundary conditions (circle). The N -point lattice is realized with log 2 N qubits, and the quantum circuit utilizes a number of quantum gates that are polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps are implemented with a number of quantum gates which are 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 one-dimensional lattice with N = 4 points.