High-fidelity non-adiabatic dark state gates for neutral atoms

Abstract

Rydberg blockade gates are the most experimentally mature entangling operations in neutral-atom quantum processors, combining fast gate times with simple control, but their performance degrades at larger interatomic separations and remains sensitive to motional and technical noise. Non-blockade gate schemes, such as dark-state and geometric protocols, offer complementary robustness but typically rely on complex and experimentally demanding control. Here we show that quantum optimal control enables non-blockade gate schemes to be implemented using the experimentally established pulse-shaping techniques developed for blockade-based gates. Focusing on the dark-state gate, we construct non-adiabatic implementations that preserve the intrinsic robustness of adiabatic dark-state protocols while achieving gate times comparable to time-optimal blockade gates using only smooth, experimentally feasible pulses. The resulting gates exhibit enhanced resilience to motional coupling, laser noise, and interaction inhomogeneity, particularly near and beyond the blockade radius. This work establishes a practical route to fast, robust two-qubit gates without increased experimental complexity.

Figures (5)

• Figure 1: Concepts of blockade, adiabatic and non-adiabatic dark state gates. (a) Schematic of the adiabatic dark state gate: to realize a dark state gate, a constant electric field is applied along the quantization axis to Stark-tune a Förster resonance. A $\pi-2\pi-\pi$ sequence is applied to the qubits to realize the gate petrosyan2017high. The level diagram including the dipole-dipole coupling of Rydberg states as well as the Rabi couplings is shown in the inset. (b) Schematic of the time optimal blockade gate: the blockade gate entirely relies on the van der Waals interaction, and only a magnetic field is applied. Due to the $1/R^{6}$ dependence of the van der Waals interaction, the interatomic distance must fall below the blockade radius, putting more stringent constraint on the interatomic distance compared to the dark state gates. On the other hand, the interatomic distance for implementing the dark state gate does not suffer from this restriction (demonstrated in the figure by having $R_{\mathrm{B}} <R_{\mathrm{DS}}$). The Rabi pulses are shaped by the application of quantum optimal control (QOC) to find time optimal pulses. The optimal pulses are global jandura2022time with the Rabi coupling equal to the maximum allowed value, whereas the phases for the control and target qubits $\varphi_{C}(t)$ and $\varphi_{T}(t)$ are shown in the inset. (c) By combining the level scheme of dark state gates with QOC pulse shaping, a non-adiabatic dark state gate is achieved. Similar to the blockade gate, the time optimal non-adiabatic dark state gate exhibits global pulses, with the Rabi frequencies set to their maximal value, and equal control and target pulse phases. This non-adiabatic gate design benefits from the advantages of both the adiabatic dark state gate and the time optimal blockade gate. The level scheme along with the detailed implementation of the CZ gate for each approach is explained in the text.
• Figure 2: Fidelity error for the CZ gate as a function of interatomic distance $R$ and implementation time $T$ (in units of $2\pi/\Omega_{\mathrm{max}}$) for (a) the non-adiabatic dark state gate, and (b) for the blockade gate. To implement the dark state gate, an electric field $E_{z} \!=\! E_{\mathrm{res}}$ is applied in the quantization direction $z$, to bring the two-atom Rydberg state $\ket{rr}$ into resonance with $\ket{(r_{+}r_{-})}$ via Stark tuning. The resonant Rydberg states are $\ket{r} \!=\! \ket{70 P_{3/2},m_j \!=\! 3/2}$, $\ket{r_{+}} \!=\! \ket{71 S_{1/2},m_j \!=\! 1/2}$ and $\ket{r_{-}} \!=\! \ket{70 S_{1/2},m_j \!=\! 1/2}$. For the limit $R \to 0$, the minimum implementation time approaches the optimal time $T_{\mathrm{opt}} \simeq 1.2113 \, \cdot 2\pi/\Omega_{\mathrm{max}}$ for the ideal blockade gate ($\Omega_{\mathrm{max}} = 2\pi \times 10 \, \mathrm{MHz}$ ), i. e. the van der Waals blockde gate with $V_{\mathrm{vdW}} \to \infty$. As the blockade radius $R_{B} \simeq 4.6 \, \mu m$ is approached, the blockade gate rapidly loses performance, while the non-adiabatic dark state gate still maintains high fidelity for implementation times $T$ comparable to $T_{\mathrm{opt}}$ at distances $R \sim 10 \, \mu m$.
• Figure 3: CZ gate error due to Rydberg state decay, as a function of the principal quantum number $n$, for the non-adiabatic dark state (blue), adiabatic dark state (orange) and the blockade (green) gates. The inset shows the time dependence of the doubly excited Rydberg state population $P_{rr}(t)$. The non-adiabaticity increases the Rydberg state population during the gate time evolution for the non-adiabatic dark state gate compared to its adiabatic counterpart. However, the unwanted population is still significantly smaller than the blockade gate. However, due to the larger decay rate of the $S_{1/2}$ states of the $^{133}$C atom compared to the $P_{3/2}$ states, the decay error is largest for the adiabatic dark state and the smallest for the time optimal blockade, with the non-adiabatic dark state gate in between. Compared to the adiabatic dark state gate, the non-adiabatic version shows increased performance.
• Figure 4: Mean infidelity due to laser phase fluctuations (thick solid lines) for the non-adiabatic dark state gate (blue) and the blockade gate (orange). The regions within one standard deviation is highlighted for each gate. While at distances $R \lesssim 3 \, \mu m$ all gates have similar fidelity errors, the blockade gate rapidly loses fidelity around $R \simeq 4 \, \mu m$, while the non-adiabatic dark state gate maintains a reasonable performance up to $R \simeq 8 \, \mu m$.
• Figure 5: Infidelity due to the shot-to-shot intensity noise, for the non-adiabatic dark state (blue), adiabatic dark state (orange), and the blockade gate (green). The performance of the non-adiabatic dark state gate is enhanced compared to the adiabatic dark state gate and becomes comparable to the blockade gate.