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We demonstrate tunable spin-spin couplings between trapped atomic ions,mediated by laser forces on multiple transverse collective modes of motion. A$\sigma_x \sigma_x$-type Ising interaction is realized between quantum bitsstored in the ground hyperfine clock states of Yb ions. We demonstrateentangling gates and tailor the spin-spin couplings with two and three trappedions. The use of closely-spaced transverse modes provides a new class ofinteractions relevant to quantum computing and simulation with largecollections of ions in a single crystal.

Entanglement and Tunable Spin-Spin Couplings Between Trapped Ions Using Multiple Transverse Modes