  Topological quantum computation based on anyons is a promising approach to
achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev
chain are an example of non-Abelian anyons where braiding operations can be
used to perform quantum gates. Here we perform a quantum simulation of
topological quantum computing, by teleporting a qubit encoded in the Majorana
zero modes of a Kitaev chain. The quantum simulation is performed by mapping
the Kitaev chain to its equivalent spin version, and realizing the ground
states in a superconducting quantum processor. The teleportation transfers the
quantum state encoded in the spin-mapped version of the Majorana zero mode
states between two Kitaev chains. The teleportation circuit is realized using
only braiding operations, and can be achieved despite being restricted to
Clifford gates for the Ising anyons. The Majorana encoding is a quantum error
detecting code for phase flip errors, which is used to improve the average
fidelity of the teleportation for six distinct states from $70.76 \pm 0.35 \% $
to $84.60 \pm 0.11 \%$, well beyond the classical bound in either case.
