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arXiv:1910.14178 · Physical Review A

Laser-free trapped-ion entangling gates with simultaneous insensitivity to qubit and motional decoherence

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

Published Apr 29, 2020• 24 citations
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Abstract

The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.

DOI
10.1103/physreva.101.042334

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The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.
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Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.
Abstract We discuss a laser-free, two-qubit geometric phase gate technique for generating high-fidelity entanglement between two trapped ions. The scheme works by ramping the spin-dependent force on and off slowly relative to the gate detunings, which adiabatically eliminates the spin-motion entanglement (AESE). We show how gates performed with AESE can eliminate spin-motion entanglement with multiple modes simultaneously, without having to specifically tune the control field detunings. This is because the spin-motion entanglement is suppressed by operating the control fields in a certain parametric limit, rather than by engineering an optimized control sequence. We also discuss physical implementations that use either electronic or ferromagnetic magnetic field gradients. In the latter, we show how to ‘AESE’ the system by smoothly turning on the effective spin-dependent force by shelving from a magnetic field insensitive state to a magnetic field sensitive state slowly relative to the gate mode frequencies. We show how to do this with a Rabi or adiabatic rapid passage transition. Finally, we show how gating with AESE significantly decreases the gate’s sensitivity to common sources of motional decoherence, making it easier to perform high-fidelity gates at Doppler temperatures.
Entangling interactions between distant qubits can be mediated via an additional degree of freedom. In conventional trapped-ion schemes, realizing a well-defined, coherent gate typically requires spectrally addressing a specific bus mode. As the ion number increases, the coupling to each individual motional mode becomes weaker, so gates on large ion strings mediated by a single mode are necessarily slow. Moreover, addressing a large number of modes demands complex driving schemes, and the fundamentally perturbative character of these approaches imposes constraints on achievable gate speed and fidelity. Here, we introduce a scheme for entangling trapped-ion qubits using a time-dependent magnetic-field gradient, in which all axial motional modes participate in mediating the interaction and the gate construction is nonperturbative. The framework can be used to implement both multi-qubit gates and two-qubit gates between arbitrary pairs in a linear ion string. Through several explicit examples, we highlight the advantages over existing magnetic-gradient schemes and show how gates on multiple ion pairs can be carried out simultaneously.
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.
Abstract A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the σ x ⊗ σ x Mølmer–Sørensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.