Abstract
We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a ‘bichromatic’ interaction picture, we show that either or geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. The gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.
Highlights
Due to their inherent uniformity and exceptional coherence properties, trapped ions are a promising platform for scalable quantum simulations and general purpose quantum computing [1,2,3,4,5,6]
We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency
Previous laser-free trapped-ion quantum logic experiments with oscillating gradients used a pair of near-field microwave gradients, symmetrically detuned about the qubit frequency, to generate the spin-motion coupling required for an entangling gate [13, 16]
Summary
Due to their inherent uniformity and exceptional coherence properties, trapped ions are a promising platform for scalable quantum simulations and general purpose quantum computing [1,2,3,4,5,6]. An alternative scheme uses microwaves and magnetic field gradients (static or oscillating) to create the desired spin-motion coupling [10,11,12,13,14,15,16,17,18] Such laser-free gates are not limited by photon scattering, and phase control is significantly easier than in the optical domain. Previous laser-free trapped-ion quantum logic experiments with oscillating gradients used a pair of near-field microwave gradients, symmetrically detuned about the qubit frequency, to generate the spin-motion coupling required for an entangling gate [13, 16]. In the work reported here, we derive two-qubit gate dynamics in the interaction picture with respect to the bichromatic microwave field already present in current experimental implementations of geometric phase gates.
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