Power operator as witness of the decoherence in the execution of the Toffoli gate in a diamond quantum computer

Abstract

The diamond quantum computer has been employed successfully for several quantum information protocols. A Hamiltonian (), 3-qubits typical diamond quantum computer is used, consisting of diagonal terms and Rabi pulses that generate the spin flit of the Toffoli gate. From such a Hamiltonian, the respective power operator dH/dt is derived and its average behavior as a function of time is calculated. To solve numerically the Schroedinger equation, it is shown both that the Toffoli gate is not executed and that the power operator is witness of the decoherence of the execution of the Toffoli gate. When the Hamiltonian depends on time, there is exchange of energy of the 3-qubit system with the environment. The latter induces decoherence of the system. It is also concluded that the Rabi pulses technology has limitations.