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 bits
stored in the ground hyperfine clock states of Yb ions. We demonstrate
entangling gates and tailor the spin-spin couplings with two and three trapped
ions. The use of closely-spaced transverse modes provides a new class of
interactions relevant to quantum computing and simulation with large
collections of ions in a single crystal.