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arXiv:1810.08300 · New Journal of Physics

Versatile laser-free trapped-ion entangling gates

R T Sutherland, R Srinivas, S. C. Burd, D Leibfried, A C Wilson, D J Wineland, D. T. C. Allcock, D. H. Slichter, Stephen B. Libby

Published Mar 1, 2019• 47 citations
arXivHTMLPDF

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.

DOI
10.1088/1367-2630/ab0be5

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We propose a σ z ⊗ σ z laser-free entangling gate which uses the intrinsic J -coupling of ions in a static magnetic gradient. Dephasing of the interaction is suppressed by means of continuous dynamical decoupling using pairs of microwave fields. The gate is virtually insensitive to common amplitude noise of the microwave fields and enables high fidelities despite qubit frequency fluctuations, while the J -coupling interaction's inherent robustness to motional decoherence is retained. Errors far below the fault-tolerant threshold can be achieved at high initial temperatures, negating the requirement of sideband cooling below the Doppler temperature. By adjusting the powers of the continuous microwave fields, the J -coupling interaction can be tuned and can be used to implement parallel entangling gates within an ion chain.
A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits’ coherence time by 3 orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states | Φ + ⟩ and | Ψ + ⟩ in less than or equal to 313 μ s with fidelities up to 98 − 3 + 2 % in a static magnetic gradient of only 19.09 T / m . At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.
A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.
A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.
We propose a pulsed dynamical decoupling protocol as the generator of tunable, fast, and robust quantum phase gates between two microwave-driven trapped-ion hyperfine qubits. The protocol consists of sequences of $\ensuremath{\pi}$ pulses acting on ions that are oriented along an externally applied magnetic-field gradient. In contrast to existing approaches, in our design the two vibrational modes of the ion chain cooperate under the influence of the external microwave driving to achieve significantly increased gate speeds. Our scheme is robust against the dominant noise sources, which are errors on the magnetic-field and microwave pulse intensities, as well as motional heating, predicting two-qubit gates with fidelities above 99.9% in tens of microseconds.
We propose a σz⊗ σzlaser-free entangling gate which uses the intrinsic J-coupling of ions in a static magnetic gradient. Dephasing of the interaction is suppressed by means of continuous dynamical decoupling using pairs of microwave fields. The gate is virtually insensitive to common amplitude noise of the microwave fields and enables high fidelities despite qubit frequency fluctuations, while the J-coupling interaction's inherent robustness to motional decoherence is retained. Errors far below the fault-tolerant threshold can be achieved at high initial temperatures, negating the requirement of sideband cooling below the Doppler temperature. By adjusting the powers of the continuous microwave fields, the J-coupling interaction can be tuned and can be used to implement parallel entangling gates within an ion chain.