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

Parallel execution of quantum gates in a long linear ion chain via Rydberg mode shaping