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

Abstract

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.

7 pages and 5 figures

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• Towards Rydberg quantum logic with trapped ions
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• Shuttling of Rydberg ions for fast entangling operations
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• Single-site Rydberg addressing in 3D atomic arrays for quantum computing with neutral atoms
• Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+
• Experimental demonstration of an efficient number diagnostic for long 1D ion chains
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• Tripartite quantum Rabi model with trapped Rydberg ions