Comparison of trapped-ion entangling gate mechanisms for mixed species
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Abstract
Entangling gates are an essential capability of quantum computers. There are different methods for implementing two-qubit gates, with respective advantages and disadvantages. We investigate the experimentally relevant differences and commonalities of laser-based $σ_z\otimesσ_z$ light-shift and $σ_φ\otimesσ_φ$ Moelmer-Soerensen gates, highlighting the phases of experimental control fields and their long-term stabilities, in the specific case of mixed-species gates. We implement these gates on qubits with very different magnetic field sensitivities, encoded in $^{43}\mathrm{Ca}^+$ and $^{88}\mathrm{Sr}^+$, achieving fidelities of $99.8\%$ for the $σ_z\otimesσ_z$ and $99.6\%$ for the $σ_φ\otimesσ_φ$ gate.