Seyed Shakib Vedaie

State-of-the-art two-qubit gates with trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Our aim is to introduce closed-loop control for two-qubit gates to correct disturbances as they occur during the gate implementation. We introduce a spectator ion into the ion chain used for quantum logic processing, where it couples with the other ions through collective motional modes. The spectator ion's position is continuously monitored by driving dipole transitions and detecting the resultant fluorescence. We show that incorporating a spectator ion is feasible for linear Paul trap implementations and is expected to reduce the two-qubit gate Bell-state preparation infidelity by an order of magnitude with the deleterious effects of position monitoring being negligible compared to the thermal effects that exist in the system, even in the absence of the spectator ions. Mathematically, we describe driven ion-trap dynamics, including the spectator ion, by a stochastic quantum master equation involving the amplitude-modulation multimode-motional coupling gate, motional drift, thermal effects, recoil from photon scattering, spontaneous decay, and light shift. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves `learning' and correcting disturbances happening in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity at a reduced calibration overhead owing to the small parameter drift in the control system.

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.