  Topological quantum computers provide a fault-tolerant method for performing
quantum computation. Topological quantum computers manipulate topological
defects with exotic exchange statistics called anyons. The simplest anyon model
for universal topological quantum computation is the Fibonacci anyon model,
which is a non-abelian anyon system. In non-abelian anyon systems, exchanging
anyons always results a unitary operations instead of a simple phase changing
in abelian anyon systems. So, non-abelian anyon systems are of the interest to
topological quantum computation. Up till now, most people still hold the belief
that topological quantum computions can be implemented only on the non-abelian
anyon systems. But actually this is not true. Inspired by extrinsic
semiconductor technology, we suggest that abelian anyon systems with defects
also support topological quantum computing. In this letter, we report a
topological quantum computer prototype based on $\mathbb{Z}_2$ abelian anyon
system.

Quantum Physics