Entanglement Generation via Single-Qubit Rotations in a Torn Hilbert Space

We propose an efficient yet simple protocol to generate arbitrary symmetric entangled states with only global single-qubit rotations in a torn Hilbert space. The system is based on spin-1/2 qubits in a resonator such as atoms in an optical cavity or superconducting qubits coupled to a main bus. By sending light or microwave into the resonator, it induces ac Stark shifts on particular angular-momentum eigenstates (Dicke states) of qubits. Then we are able to generate barriers that hinder transitions between adjacent Dicke states and tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes highly nontrivial, and thus generates entanglement among the many-body system. By optimal control of energy shifts on Dicke states, we are able to generate arbitrary symmetric entangled states. We also exemplify that we can create varieties of useful states with near-unity fidelities in only one or very few steps, including W states, spin-squeezed states (SSSs), and Greenberger-Horne-Zeilinger states. Particularly, the SSS can be created by only one step with a squeezing parameter ${\xi }_R^2\sim 1/N^{0.843}$ approaching the Heisenberg limit. Our finding establishes a way for universal entanglement generations with only single-qubit drivings where all the multiple-qubit controls are integrated into simply switching on or off microwave. It has direct applications in the variational quantum optimizer, which is available with existing technology.