Versatile laser-free trapped-ion entangling gates.

Area of Science:

• Quantum Information Science
• Atomic, Molecular, and Optical Physics
• Quantum Computing

Background:

• Trapped-ion hyperfine qubits are promising for quantum computation.
• Developing laser-free methods for quantum gates is crucial for scalability.
• Geometric phase gates offer robust quantum operations.

Purpose of the Study:

• To present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits.
• To demonstrate the feasibility of performing specific geometric phase gates (${\hat{\sigma }}_{\varphi }\otimes {\hat{\sigma }}_{\varphi }$ and ${\hat{\sigma }}_z\otimes {\hat{\sigma }}_z$).
• To explore intrinsic dynamical decoupling from qubit frequency fluctuations.

Main Methods:

• Utilizing static or oscillating magnetic-field gradients.
• Employing a pair of uniform microwave fields symmetrically detuned about the qubit frequency.
• Transforming into a 'bichromatic' interaction picture.

Main Results:

• Demonstrated the performance of ${\hat{\sigma }}_{\varphi }\otimes {\hat{\sigma }}_{\varphi }$ and ${\hat{\sigma }}_z\otimes {\hat{\sigma }}_z$ geometric phase gates.
• Showed that gate basis is determined by microwave detuning.
• Identified tunable driving parameters for dynamical decoupling.
• Proposed a novel implementation for ${\hat{\sigma }}_z\otimes {\hat{\sigma }}_z$ gates easing experimental constraints.

Conclusions:

• The proposed laser-free method provides a viable route for implementing entangling gates.
• The technique offers intrinsic robustness against qubit frequency fluctuations.
• Numerical simulations indicate high gate fidelities with realistic parameters.