Implementation of the Fredkin gate with a three-qubit mixed-spin Heisenberg model

We show that a local unitary (LU) equivalent Fredkin gate can be obtained from the free evolution of three mixed-spin qubits by virtue of numerical simulation with only one step. The spin-1 qubit acts as the control qubit, and two spin-1/2 qubits, which interact with the spin-1 qubit via the first neighbor spin interaction, respectively, play the role of target qubits. We also examine the imperfect Fredkin gate operation by considering the effects of nonidentical coupling constants, uniform and inhomogeneous magnetic fields.