Synthesis of some three-qubit gates and their implementation in a three spins system coupled with Ising interaction

The synthesis of the Toffoli gate, Fredkin gate, three-qubit Inversion-on-equality gate and D(alpha) gate, as well as their implementation in a three spins system coupled with Ising interaction are investigated. The sequences of the control pulse and the drift process to implement these gates are given. It is revealed that the implementation of some three-qubit gates in a circular spin chain is much better than in a linear spin chain, and every two measurements of the quantum computation complexity are not always consistent. It is significant to directly study the implementation of the multi-qubit gates and even more complicated components of quantum information processing without resorting to their synthesis.