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

TL;DR

This paper presents a method to physically realize topological quantum walks on finite lattices using a logarithmic number of qubits, demonstrating topological features experimentally on IBM-Q hardware.

Contribution

It introduces an efficient quantum circuit implementation of topological quantum walks that scales polynomially and demonstrates topological phenomena on real quantum hardware.

Findings

Successfully implemented topological quantum walks on IBM-Q.

Observed boundary bound states experimentally.

Scalable quantum circuit design for topological phenomena.

Abstract

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.