  We present a mechanism that permits the parallel execution of multiple
quantum gate operations within a single long linear ion chain. Our approach is
based on large coherent forces that occur when ions are electronically excited
to long-lived Rydberg states. The presence of Rydberg ions drastically affects
the vibrational mode structure of the ion crystal giving rise to modes that are
spatially localized on isolated sub-crystals which can be individually and
independently manipulated. We theoretically discuss this Rydberg mode shaping
in an experimentally realistic setup and illustrate its power by analyzing the
fidelity of two conditional phase flip gates executed in parallel. Our scheme
highlights a possible route towards large-scale quantum computing via
vibrational mode shaping which is controlled on the single ion level.
