Hybrid Microwave-Radiation Patterns for High-Fidelity Quantum Gates with Trapped Ions

We present a method that combines continuous and pulsed microwave-radiation patterns to achieve robust interactions among hyperfine trapped ions placed in a magnetic field gradient. More specifically, our scheme displays continuous microwave drivings with modulated phases, phase flips, and $\pi$ pulses. This leads to high-fidelity entangling gates that are resilient against magnetic field fluctuations, changes in the microwave amplitudes, and crosstalk effects. Our protocol runs with arbitrary values of microwave power, which includes the technologically relevant case of low microwave intensities. We demonstrate the performance of our method with detailed numerical simulations that take into account the main sources of decoherence.

Figure 1

Resilience to constant errors for $g_B=20.9\mathrm{T}/\mathrm{m}$, $\nu =2\pi \times 138$ kHz ($\eta =0.011$), and $\mathrm{\Omega }=2\pi \times 26$ kHz. (a) Bell-state fidelity for ${\mathrm{\Omega }}_{\mathrm{DD}}=0$ (dashed blue curve) and ${\mathrm{\Omega }}_{\mathrm{DD}}=2\pi \times 49$ kHz (solid green curve). The right and left panels show the cases with and without phase modulation, respectively. (b) Bell-state fidelity for $n_{\mathrm{PF}}=1$ (solid green curve) and for $n_{\mathrm{PF}}=0$ (dashed red curve). (c) Bell-state fidelity with respect to constant shifts in $\mathrm{\Omega }(t)$.

Figure 2

Scheme for the control parameters. (a) Bichromatic driving $\mathrm{\Omega }(t)=\mathrm{\Omega }\cos \delta t$. (b) Phase modulation of the bichromatic driving. The change of sign during the second half of the evolution is due to the phase flip of the carrier driving. Here ${\varphi }_m=max[|\varphi (t)|]$. (c) Carrier driving acting equivalently on both ions except in the middle, where each ion undergoes a ${180}^{\circ }$ (red) and a ${360}^{\circ }$ (green) rotation, respectively. (d) Phase modulation of the DD field. During the second part of the evolution, the phase is flipped from $-\pi /2$ to $\pi /2$.

Figure 3

Logarithm of the Bell-state infidelity as a function of ${\mathrm{\Omega }}_{\mathrm{DD}}$ for $g_B=20.9$ T/m, $\nu =2\pi \times 138$ kHz, and $\mathrm{\Omega }=2\pi \times 37\mathrm{kHz}$ (left panel) and $g_B=38.5$ T/m, $\nu =2\pi \times 207$ kHz, and $\mathrm{\Omega }=2\pi \times 26.6$ kHz (right panel). Blue and black squares take into account crosstalk effects and the presence of the off-resonant vibrational mode, with and without phase modulation, respectively. Other curves include motional heating of the center-of-mass mode and fluctuations of the magnetic field as well as the driving fields. The red, green, and purple squares correspond to different error parameters ($\tau =0.05$ ms and $T_2=0.5$ ms; $\tau =0.1$ ms and $T_2=1$ ms; and $\tau =0.2$ ms and $T_2=2$ ms) that characterize magnetic field fluctuations.