Protected two-qubit entangling gate with mechanical driven continuous dynamical decoupling

Abstract

In this work, we propose a high-fidelity phonon-mediated entangling gate in a hybrid mechanical system based on two silicon-vacancy color centers in diamond. In order to suppress the influence of the spin decoherence on the entangling gate, we use continuous dynamical decoupling approach to create new dressed spin states, which are less sensitive to environmental fluctuations and exhibit an extended $T_{2}^*$ spin dephasing time. The effective spin-spin Hamiltonian modified by the mechanical driving field and the corresponding master equation are derived in the dispersive regime. We show that in the presence of the mechanical driving field, the effective spin-spin coupling can be highly controlled. By calculating the entangling gate fidelity in the dressed basis, we find that once the mechanical field is turned on, the gate fidelity can be significantly improved. In particular, under an optimized spin-phonon detuning and a stronger Rabi frequency of the mechanical driving field, the two-qubit gate is capable of reaching fidelity exceeding $0.99$. Moreover, by employing appropriate driving modulation, we show that a high-fidelity full quantum gate can be also realized, in which the initial and final spin states are in bare basis. Our work provides a promising scheme for realizing high-fidelity quantum information processing.