Multipartite controlled-NOT gates using molecules and Rydberg atoms

Abstract

We propose high-fidelity controlled-NOT (CNOT) gates in a hybrid system of polar molecules and Rydberg atoms based on the unconventional Rydberg pumping mechanism. By combining the rich internal structure of polar molecules with the strong dipole-dipole interactions of Rydberg atoms, we realize both two-to-one and one-to-two gate configurations. Numerical simulations show that the gate performance is robust against spontaneous emission from Rydberg states. The approach naturally extends to larger systems, as demonstrated by four-qubit implementations achieving three-to-one and one-to-three CNOT gates with fidelities exceeding 99\%. These results highlight hybrid molecule-Rydberg atom architectures as a promising platform for scalable quantum information processing.

Figures (9)

• Figure 1: System configuration and operational mechanism of the hybrid many-to-one CNOT gate. (a) Spatial arrangement of the $^{87}\mathrm{Rb}$ atom and $\mathrm{CaF}$ molecules. Two molecules (control qubits, left and right) and a central Rydberg atom (target qubit) are aligned linearly, with the atom positioned equidistant from the molecules. (b) Energy-level structure of the molecule–atom system. The molecule contains three states $|0\rangle$, $|1\rangle$, and $|2\rangle$. The atom involves two ground states $|g\rangle$, $|e\rangle$, and two Rydberg states $|R\rangle$, $|r\rangle$. The green lines represent the transition dipole moments that mediate the interaction. The red and blue arrows denote the laser fields with Rabi frequencies $\Omega_1$ and $\Omega_2$, respectively, which couple the atomic ground states to the Rydberg state $|r\rangle$. (c) Transition pathways in different subspaces. $V$ denotes the strength of the molecule–atom dipole–dipole interaction.
• Figure 2: Dynamics of the hybrid two-to-one CNOT gate driven by Gaussian pulses. (a) The populations of the relevant basis states and the control pulse. (b) Time evolution of the fidelity. The blue solid line and the orange open circles represent the dynamics governed by the full Hamiltonian and the effective Hamiltonian, respectively. The system is driven by Gaussian pulses defined as $\Omega_1=-\Omega_2=\Omega=\Omega_{\text{max}} \exp[^{-(t-t_0)^2/(2\sigma^2)}]$, where the maximum Rabi frequency is $\Omega_{\text{max}} = 2\pi \times 1.05$ MHz and the pulse width is $\sigma = 0.27 \mu$s. The molecule–atom interaction strength is set to $V = 2\pi \times 4.04$ MHz.
• Figure 3: System configuration and operating mechanism of the hybrid one-to-many CNOT gate. (a) Spatial arrangement where two Rydberg atoms (target qubits) are positioned symmetrically on either side of a central molecule (control qubit). (b) Relevant energy-level structures. The molecular energy levels are the same as those shown in Fig. \ref{['Figure1']}(b). For the atoms, two laser fields with Rabi frequencies $\Omega_1$ (red arrow) and $\Omega_2$ (blue arrow) drive transitions from the ground states to the Rydberg state $|r\rangle$ with a detuning $\Delta$. (c) Transition pathways in different subspaces. The upper panels correspond to the case where the control molecule is in state $|0\rangle$, while the lower panels correspond to the case where the molecule is in state $|1\rangle$.
• Figure 4: Dynamics of the hybrid one-to-two CNOT gate driven by Gaussian pulses. (a) The populations of the relevant basis states and the control pulse. (b) Time evolution of the fidelity. The van der Waals interaction strengths are $U_1 = 2\pi \times 1774.6$ MHz and $U_2 = 2\pi \times 126.9$ MHz. The other parameters are $\Omega_{\text{max}} = 2\pi \times 0.71$ MHz, $\Delta = 2\pi \times 2$ MHz, and $\sigma = 2.25 \mu$s.
• Figure 5: Time evolution of the gate fidelity governed by the master equation. The blue curve corresponds to the non-dissipative case, while the red open circle includes the effect of spontaneous decay from Rydberg states. The insets show a magnified view of the fidelity overlap. The decay rates are set to $\gamma_1 = 2\pi \times 4.580$ kHz and $\gamma_2 = 2\pi \times 2.393$ kHz. (a) Hybrid two-to-one CNOT gate, with the other parameters the same as those in Fig. \ref{['Figure2']}. (b) Hybrid one-to-two CNOT gate, with the other parameters the same as those in Fig. \ref{['Figure4']}.