Halving ion-trap two-qubit gate time while enhancing frequency-drift robustness

Two-qubit gate performance is vital for scaling up ion-trap quantum computing, and reducing gate time τ and gate error rate is achieved by quantum-control methods. We develop a full model for two-qubit gates effected in a Paul trap with multiple ions, described by a master equation incorporating the single-ion quadrupolar effective Rabi frequency,

an Autler-Townes shift, off-resonant transitions, photon scatterings, laser-power fluctuations, motional heating, cross-Kerr phonon coupling and laser spillover with no fitting parameters. To minimize τ, while maintaining fixed gate fidelity, we articulate and solve the feasibility problem: given the seven-ion master equation with all ions prepared in the ground state and given vibrational modes initially in a ∼μK thermal state, and with the target being two of the ions evolving over time τ into a Bell state, and subject to a strict upper bound on laser power, design an amplitude-modulated Raman laser pulse that deterministically yields a close approximation to this Bell state. We solve our problem by global optimization and obtain a pulse sequence that executes in half the time required by state-of-the-art methods. Our pulse is robust against long-term drift in the frequency detuning and an imperfect initial motional ground state.