Noisy Multiple-Control Fredkin Gate in Nuclear Spin Based Qubits Chain

The Fredkin gate is a reversible self-inverse logic gate that maintains parity, so it is widely used in DNA computing, low-power CMOS, quantum computing, and nanotechnology. The paper proposes a design of the multiple-control Fredkin gate based on the model of a chain of atoms with nuclear spins one-half in a spinless semiconductor matrix. The allowed transitions realizing the gate operation for two π-pulses are analyzed. The effect of frequency noise and decoherence on the fidelity of the multiple-control Fredkin gate are discussed.