Versatile laser-free trapped-ion entangling gates

Abstract

Wepresent 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 showthat either 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 fromqubit frequency fluctuations. The gates can be implemented in a novel manner which eases experimental constraints.Wepresent numerical simulations of gate fidelities assuming realistic parameters.