Versatile laser-free trapped-ion entangling gates

TL;DR

This paper introduces a comprehensive theory for implementing versatile laser-free entangling gates in trapped-ion systems using magnetic-field gradients and microwave fields, enabling flexible, robust quantum gate operations.

Contribution

It develops a general framework for laser-free entangling gates with trapped ions, including novel implementations and tunable gate bases, with detailed numerical fidelity analysis.

Findings

Both ${\

sigma_phi} \

sigma_z} gates can be realized using this method.

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 ${\hat{\sigma}_{\phi}\otimes\hat{\sigma}_{\phi}}$ or ${\hat{\sigma}_{z}\otimes\hat{\sigma}_{z}}$ 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 ${\hat{\sigma}_{z}\otimes\hat{\sigma}_{z}}$ gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.