Scaling Ion Trap Quantum Computation through Fast Quantum Gates

We propose a method to achieve scalable quantum computation based on fast quantum gates on an array of trapped ions, without the requirement of ion shuttling. Conditional quantum gates are obtained for any neighboring ions through spin-dependent acceleration of the ions from periodic photon kicks. The gates are shown to be robust to influence all the other ions in the array and insensitive to the ions' temperature.

Figure 1

A possible geometry of the ion array for scalable quantum computing from multiconnected linear Paul traps. Conditional quantum gates are achieved for any neighboring ions though application of a spin-dependent kicking force on these two ions. (b). The typical trajectory of the kicked ion in phase space, where “+” denotes the initial position, ”○” and “×” denote the final position of the ion in $|0\rangle$ or $|1\rangle$ states, which in general is different from the initial position as the ion has an initial velocity.

Figure 2

The sequence of the spin-dependent kicking force for the one-cycle (a), two-cycle (b), and four-cycle (c) schemes, with $t_2=t_1/2^{1/5}$ and $t_3=t_1/2^{2/5}$. The solid (dashed) curves are, respectively, for the ions in $|0\rangle$ or $|1\rangle$ states.

Figure 3

The gate time $T_g$ for the controlled phase flip operation is shown as a function of the repetition frequency of the kicking laser pulses for the ${}^{111}\mathrm{C}\mathrm{d}^{+}$ (solid curve), ${}^{40}\mathrm{C}\mathrm{a}^{+}$ (dotted curve), and ${}^9\mathrm{B}\mathrm{e}^{+}$ (dashed curve) ions, where the neighboring ions' distance $d$ is taken as $d=10\mu \mathrm{m}$, and the carrier wave length for the ${}^{111}\mathrm{C}\mathrm{d}^{+}$, ${}^{40}\mathrm{C}\mathrm{a}^{+}$, and ${}^9\mathrm{B}\mathrm{e}^{+}$ ions are assumed to be 215 nm, 393 nm, and 313 nm, respectively. (b) The scaling parameter ${\omega }_l{T}_g$ in the gate fidelity is shown as a function of the neighboring ions' distance $d$ for ${}^{111}\mathrm{C}\mathrm{d}^{+}$ with the pulse repetition frequency $f_r=1\mathrm{G}\mathrm{H}\mathrm{z}$ (dashed curve) and $f_r=10\mathrm{G}\mathrm{H}z$ (solid curve), respectively. The curve is well fit by the scaling ${\omega }_l{T}_g\propto d^{-9/10}$.