Fast, Accurate, and Realizable Two-Qubit Entangling Gates by Quantum Interference in Detuned Rabi Cycles of Rydberg Atoms. (arXiv:1809.08957v2 [quant-ph] UPDATED)

High-fidelity entangling quantum gates based on Rydberg interactions are
required for scalable quantum computing with neutral atoms. Their realization,
however, meets a major stumbling block -- the motion-induced dephasing of the
transition between the ground and Rydberg states. By using quantum interference
between different detuned Rabi oscillations, we propose a practical scheme to
realize a class of accurate entangling Rydberg quantum gates subject to a
minimal dephasing error. We show two types of such gates, $U_{1}$ and $U_{2}$,
in the form of $\text{diag}\{1, e^{i\alpha}, e^{i\gamma}, e^{i\beta}\}$, where
$\alpha, \gamma$, and $\beta$ are determined by the parameters of lasers and
the Rydberg blockade $V$. $U_{1}$ is realized by sending to the two qubits a
single off-resonant laser pulse, while $U_{2}$ is realized by individually
applying one pulse of detuned laser to each qubit. Our method has several
advantages. First, the gates are accurate because the fidelity of $U_k$ is
limited only by a rotation error below $10^{-5}$ and the Rydberg-state decay.
Decay error on the order of $10^{-5}$ can be easily obtained because all
transitions are detuned, resulting in small population in Rydberg state.
Second, the motion-induced dephasing is minimized because there is no gap time
in which a population is left in the Rydberg shelving states of either qubit.
Third, the gate is resilient to the variation of $V$. This is because among the
three phases $\alpha,\gamma$, and $\beta$, only the last has a (partial)
dependence on $V$. Fourth, the Rabi frequency and $V$ in our scheme are of
similar magnitude, which permits a fast implementation of the gate when both of
them are of the feasible magnitude of several megahertz. The rapidity,
accuracy, and feasibility of this interference method can lay the foundation
for entangling gates in universal quantum computing with neutral atoms.

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