Transverse Polarization Gradient Entangling Gates for Trapped-Ion Quantum Computation

The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam, previously proposed as a Magnus-type quantum logic gate. Using this technique, we perform Raman operations on nuclear spin qubits encoded in 171Yb+ ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve MS gates with fidelities exceeding 98.5% (97.2%). Further improvements in numerical aperture and laser power could reduce gate durations while enhancing fidelity. This method is compatible with, and can significantly simplify, optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be extended to two-dimensional ion crystals, representing a key step toward large-scale trapped-ion quantum processors.