Minimum unit for the fractional statistics of anyons and its application

Although Han et al. [ Phys. Rev. Lett. 98 150404 (2007)] proposed a quantum circuit with six qubits to demonstrate the basic braiding statistics of anyons, we have found that a four-qubit system is enough for realizing such a process. We call it the minimum unit for the fractional statistics of anyons. With some special order, the minimum unit can be used to construct two kinds of fractional charge excitation n/(n+1) [or (n+1)/n] and (n²-kn+6n+2)/(n²-kn+5n+4) [or (n²-kn+2n+k+1)/3(n²-kn+5n+4)], where n,k are positive integers and k⩽n. This minimum unit can be realized by a photonic quantum simulator or by electrons in an optical lattice or quantum dot array. Its use will have some advantages in metrology.