Trapped Ion Quantum Computing Using Optical Tweezers and Electric Fields

We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground-state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.

Figure 1

(a) Schematic representation of a linear chain of ions where optical tweezers are applied to ions $i$ and $j$. The tweezers shift the c.m. mode depending on the internal state of the pair. (b) Level scheme of the four states; only the states $|01⟩$ and $|10⟩$ are unaffected by the extra trapping potential generated by the tweezers. (c) Phase space dynamics of the four states when adding an electric field at a frequency ${\omega }_{\mathrm{com}}-\delta$. Because of the displacement generated by the driving electric field, the states $|01⟩$ and $|10⟩$ acquire a phase $\varphi$.

Figure 2

(a) Pulse sequence used for the simulations; $E(t)/E_0$ and $I(t)/I_0$ are the normalized electric field and laser intensities, respectively. At the end of each of the first three pulses, we perform a $\pi$ pulse on either ion 1 or 2. (b) Phase space dynamics for a two-ion crystal in natural units. When the ions are in the state $|01⟩$ or $|10⟩$, the electric field makes them oscillate. For the states $|11⟩$ and $|00⟩$, the electric field is not resonant with the c.m. mode. The residual motion of states $|11⟩$ and $|00⟩$ is highlighted in the insets. The parameters used are $\delta =2\pi \times 0.001\mathrm{MHz}$, $E_0=0.269\mathrm{mV}/\mathrm{m}$, ${\omega }_{\mathrm{com}}=2\pi \times 1\mathrm{MHz}$, and ${\omega }_{\mathrm{tw}}=2\pi \times 250\mathrm{kHz}$.

Figure 3

Process fidelity as a function of tweezer strength for a two-ion crystal at different $\delta$ and $\overline{n}$ at ${\omega }_{\mathrm{com}}=2\pi \times 1\mathrm{MHz}$. The resulting gate time is $4\tau$ with $\tau =2\pi /\delta$. The green pentagons show the fidelity for a two-ion crystal taking into account the contribution of both modes. The Fock-state cutoff for the thermal state used in the calculations is $n_{\max }=20$ for the single-mode cases with $\overline{n}\le 1$ and $n_{\max }=100$ for $\overline{n}\simeq 10$. For the two modes case $n_{c,\max }=14$ and $n_{s,\max }=10$, with ${\overline{n}}_c$ and ${\overline{n}}_s$, respectively, the average phonon number in the c.m. and stretch mode.

Figure 4

Effect of noise $\mathrm{\Lambda }$ on the tweezer laser intensity at frequencies ${\nu }_{\mathrm{\Lambda }}=1/\tau$ and shot-to-shot noise (${\nu }_{\mathrm{\Lambda }}=0$) for ${\omega }_{\mathrm{tw}}\sim 2\pi \times 180\mathrm{kHz}$, $\delta =2\pi \times 1\mathrm{kHz}$, and ${\omega }_c=2\pi \times 1\mathrm{MHz}$. The points at ${\nu }_{\mathrm{\Lambda }}=1/\tau$ are taken assuming a random Gaussian noise for each of the four gate pulses with a standard deviation $\sigma ={\mathrm{\Lambda }}_{1/\tau }$. The points at ${\nu }_{\mathrm{\Lambda }}=0$ assume a change in the tweezer intensity ${\mathrm{\Lambda }}_{\mathrm{dc}}$ for times longer than the gate time $\tau$.