Quantum computing architecture with trapped ion crystals and fast Rydberg gates

Abstract

Fast entangling gate operations are a fundamental prerequisite for quantum simulation and computation. We propose an entangling scheme for arbitrary pairs of ions in a linear crystal, harnessing the high electric polarizability of highly excited Rydberg states. An all-to-all quantum gate connectivity is based on an initialization of a pair of ions to a superposition of ground and Rydberg states by laser excitation, followed by the entangling gate operation, which relies on a state-dependent frequency shift of collective vibrational modes of the crystal. This gate operation requires applying an electric waveform to trap electrodes. Employing transverse collective modes of oscillation, we reveal operation times on the order of microseconds within any of the qubit pairs in a small crystal. In our calculation, we take into account realistic experimental conditions and feasible electric field ramps. The proposed gate operation is ready to be combined with a scalable processor architecture to reconfigure the qubit register, either by shuttling ions or by dynamically controlling optical tweezer potentials.