Quantum logic control and entanglement in hybrid atom-molecule arrays

TL;DR

The authors address slow molecule-state readout and weak inter-molecular interactions that hinder scalable entanglement in ultracold molecular systems. They introduce a hybrid atom–molecule platform where fast, high-fidelity atom–molecule gates and atomic ancilla measurements enable rapid, scalable entangling operations, including a molecule–atom CZ gate mediated by resonant dipole–dipole exchange between molecular rotational and atomic Rydberg transitions. This approach underpins measurement-based generation of long-range molecular entanglement, notably GHZ states, and extends to high-dimensional qudit encoding and topological order, with potential realization in near-term experiments. The work demonstrates how measurement and feedforward, combined with hybrid interactions, can overcome molecule-specific limitations and unlock applications in quantum metrology, simulation, and quantum information processing in polar-molecule systems.

Abstract

Polar molecules, with their rich internal structure, offer immense potential for fundamental physics, quantum technology, and controlled chemistry. However, their utilization is currently limited because of slow and imperfect state detection and weak dipolar interaction, limiting fast and large-scale entanglement generation. We propose and analyze a scheme for quantum logic control and measurement-based state preparation in a hybrid platform of polar molecules and neutral atoms. The method leverages fast, high-fidelity atom-molecule gates and high-fidelity atomic ancilla measurements to overcome the common challenges in molecule-only platforms, while preserving their diverse structural advantages. The proposed atom-molecule controlled-phase gate is based on resonant dipole-dipole exchange between a molecular rotational transition and an atomic Rydberg transition, rendering it three orders of magnitude faster than any direct molecule-molecule entangling gate. We further study several applications of our scheme including the preparation of molecular GHZ states for quantum enhanced precision measurements, the preparation of exotic molecular qudit states with topological order, and measurement-altered criticality. Our scheme is applicable to any polar molecule. It expands the paradigm of quantum logic control and paves the way to large-scale molecular entangled states. More generally, it highlights a concrete hybrid quantum system in which each qubit is utilized in an optimal way and where the measurement-based approach can yield a significant advantage in near-term devices.

Figures (2)

• Figure 1: A controlled-phase gate between a molecule and an atom.(a)$\ket{0}$, $\ket{1}$ and $\ket{2}$ are molecular states, $\ket{1}$ and $\ket{2}$ are connected with an electric dipole transition. $\ket{a}$ and $\ket{b}$ are low-lying atomic states. $\ket{r}$ and $\ket{R}$ are atomic Rydberg states which are connected with an electric dipole transition. The transition frequency of $\ket{r}\leftrightarrow\ket{R}$ can be tuned by an electric field to near resonance with $\ket{1}\leftrightarrow\ket{2}$. A laser field couples $\ket{a}\leftrightarrow\ket{r}$. (b) The gate sequence consists of a sinusoidal-shaped laser pulse applied to the atom. When $\Delta=0$ and the pulse area is $2\pi$, it is a controlled Z gate. The maximum coupling strength $\Omega_\mathrm{L,max} \lesssim V_\mathrm{MA}$. For the pair state initially in $\ket{0a}$, the system acquires a $\pi$ phase after a Rabi oscillation to $\ket{0r}$ (middle Bloch sphere). For $\ket{1a}$, the system follows the eigenstate adiabatically and returns to $\ket{1a}$ without an extra phase (left Bloch sphere). $\ket{0b}$ and $\ket{1b}$ are not coupled by the laser and stay in the same states. When $\Delta\neq 0$ it is a controlled arbitrary phase gate. For the pair state initially in $\ket{0a}$, by choosing an appropriate pulse shape, the system undergoes an off-resonant Rabi oscillation and returns to $\ket{0a}$ with a closed loop on the Bloch sphere (right Bloch sphere). For other initial states, it is similar to the $\Delta=0$ case.
• Figure 2: Atomic ancilla measurement-based generation of a long-range entangled state of molecules. All atoms and molecules are initialized in $\ket{+}$ (for atoms $\ket{\pm} = \frac{1}{\sqrt{2}} (\ket{0} \pm \ket{1})$, for molecules $\ket{\pm} = \frac{1}{\sqrt{2}} (\ket{a} \pm \ket{b})$). Atoms are first moved to entangle with the molecules on their left side and then with the molecules on their right side. A cluster state is generated. Subsequently, all atoms are measured in the $\ket{\pm}$ basis. The subsystem of molecules is projected to a long-range entangled state, which is correlated with the states of the atoms. Based on the measurement results of the atoms, the molecular state can be rotated to the target long-range entangled state (e.g. the GHZ state) by single molecule rotations.