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arXiv:1301.3786 · Physical Review Letters

Demonstration of a Dressed-State Phase Gate for Trapped Ions

Ting Rei Tan, John Gaebler, R. Bowler, Yiheng Lin, John D. Jost, D. Leibfried, D. J. Wineland

Published Jun 26, 2013• 75 citations
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Abstract

We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.

DOI
10.1103/physrevlett.110.263002

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We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.
Quantum entangling logic gates are key ingredients for the implementation of a quantum information processing device. In this thesis, we focus on experimental implementations of three types of entangling geometric-phase gates with trapped ions, which rely on the effective spin-spin interactions generated with state-dependent forces. First, a mixed-species entangling gate is demonstrated using a 9Be+ and a 25Mg+ ion to create a Bell state with a fidelity of 0.979(1). Combined with single-qubit gates, we use this mixed-species gate to implement controlled-NOT and SWAP gates. Second, we implement a high-fidelity universal gate set with 9Be+ ions. Single-qubit gates with error per gate of 3.8(1)x10-5 are achieved. By creating a Bell state with a deterministic two-qubit entangling gate, we deduce a gate error as low as 8(4)x10-4. Third, a novel two-qubit entangling gate with dynamical decoupling built-in is demonstrated with a fidelity of 0.974(4). This gate is robust against qubit dephasing errors and offers simplifications in experimental implementation compared to some other gates with trapped ions. Errors in the above implementations are evaluated and methods to further reduce imperfections are discussed. In a separate experiment, correlated measurements made on pairs of ions violate a "chained" Bell inequality obeyed by any local-realistic theory. The lowest chained Bell inequality parameter determined from our measurements is 0.296(12), this value is significantly lower than 0.586, the minimum value derived from a perfect Clauser-Horne-Shimony-Horne (CHSH) Bell inequality experiment. Furthermore, our CHSH Bell inequality results provide a device-independent certification of the deterministically created Bell states.
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.
Abstract We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven gate is generated by a pulsed dynamical decoupling sequence applied to the ions’ carrier transitions only. It allows for a tunable phase shift with high-fidelity results. The conditional phase shift is measured using a Ramsey-type measurement with an inferred fringe contrast of up to 99 − 2 + 1 % . We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation < 20 phonons, trap frequency errors of +10%, and pulse area errors of −8%. The phase shift is not significantly affected up to < 10 phonons and pulse area errors of −2%. Both, contrast and phase shift are robust to timing errors up to −30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of 100 µ s) by using two axial motional modes of a two-ion crystal through improved setups.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.
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.