  Two-qubit gate performance is vital for scaling up ion-trap quantum
computing. Optimized quantum control is needed to achieve reductions in
gate-time and gate error-rate. We describe two-qubit gates with addressed Raman
beams within a linear trapped-ion chain by a quantum master equation (QME). The
QME incorporates the single-ion two-photon effective Rabi frequency,
Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant
transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional
heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing
beams and an imperfect initial motional ground state, with no fitting
parameters. Whereas state-of-the-art methods are oblivious to these effects in
the gate design procedure. We employ global optimization to design pulse
sequences for achieving a robust rapid two-qubit gate for seven trapped
$^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions.
Here, robust means resilient against slow drift of motional frequencies, and
rapid means gate execution where the effective Rabi frequency is comparable to
the detuning of the laser from the ion's bare electronic transition. Our robust
quantum control delivers rapid high-quality two-qubit gates in long ion chains,
enabling scalable quantum computing with trapped ions.

Quantum Physics