Fast, Accurate, and Realizable Two-Qubit Entangling Gates by Quantum Interference in Detuned Rabi Cycles of Rydberg Atoms

Abstract

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, U1 and U2, in the form of diag{1, e iα , e iγ , e iβ }, where α, γ, and β are determined by the parameters of lasers and the Rydberg blockade V . U1 is realized by sending to the two qubits a single off-resonant laser pulse, while U2 is realized by individually applying one pulse of detuned laser to each qubit. One can construct the controlled-z (CZ) gate from several U1 when assisted by single-qubit rotations and phase gates, or from two U2 and two phase gates. 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 α, γ, and β, 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.

Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field

“…(iii) will be illustrated later. As for (iv) and (v), we assume that 87 Rb atoms are adopted and the related energy levels are chosen as |0 = |5S 1/2 , F = 1, m F = 0 , |1 = |5S 1/2 , F = 2, m F = 0 , and |r = |100S 1/2 , m J = 1/2, m I = 3/2 [27]. For such Rydberg atoms, the vdWI coefficient is C 6 = 2π × 56.2 THz µm 6 [28,29].…”

“…3, the adopted parameters indicate V vdw ∼ 100Ω eff and V vdw ∼ 10δ. For the RAB CZ gate, 1% deviation in V vdw results in the offresonant |11 ↔ |rr transition with the detuning being of the same order as Ω eff , which greatly spoils the complete Rabi cycles [27] and then reduces significantly the gate fidelity by over 0.5. However for the RAB-broken gate, 1% deviation in V vdw results in ∼ 10% deviation in δ.…”

Rydberg quantum computation with nuclear spins in two-electron neutral atoms

“…To avoid exciting |0 to the Rydberg state, it is desirable to realize a generalized Rabi frequency Ω = Ω 2 1r + ∆ 2 which is 2N times Ω 1r , where N is an integer. As can be easily proved [34,98], with a duration t π of the Rydberg lasers, the input state |0 undergoes N detuned Rabi cycles, evolving to…”

Transition Slow-Down by Rydberg Interaction of Neutral Atoms and a Fast Controlled-not Quantum Gate

“…[43,81] (Ref. [81] proposed two gates among which the first is quoted here). Compared to the initial interference method, Ref.…”