  Electrons are indivisible elementary particles, yet paradoxically a
collection of them can act as a fraction of a single electron, exhibiting
exotic and useful properties. One such collective excitation, known as a
topological Majorana mode, is naturally stable against perturbations, such as
unwanted local noise, and can thereby robustly store quantum information. As
such, Majorana modes serve as the basic primitive of topological quantum
computing, providing resilience to errors. However, their demonstration on
quantum hardware has remained elusive. Here, we demonstrate a verifiable
identification and braiding of topological Majorana modes using a
superconducting quantum processor as a quantum simulator. By simulating
fermions on a one-dimensional lattice subject to a periodic drive, we confirm
the existence of Majorana modes localized at the edges, and distinguish them
from other trivial modes. To simulate a basic logical operation of topological
quantum computing known as braiding, we propose a non-adiabatic technique,
whose implementation reveals correct braiding statistics in our experiments.
This work could further be used to study topological models of matter using
circuit-based simulations, and shows that long-sought quantum phenomena can be
realized by anyone in cloud-run quantum simulations, whereby accelerating
fundamental discoveries in quantum science and technology.
