Global entangling gates on arbitrary ion qubits

Abstract

Quantum computers can efficiently solve classically intractable problems, such as the factorization of a large number1 and the simulation of quantum many-body systems2,3. Universal quantum computation can be simplified by decomposing circuits into single- and two-qubit entangling gates4, but such decomposition is not necessarily efficient. It has been suggested that polynomial or exponential speedups can be obtained with global N-qubit (N greater than two) entangling gates5,6,7,8,9. Such global gates involve all-to-all connectivity, which emerges among trapped-ion qubits when using laser-driven collective motional modes10,11,12,13,14, and have been implemented for a single motional mode15,16. However, the single-mode approach is difficult to scale up because isolating single modes becomes challenging as the number of ions increases in a single crystal, and multi-mode schemes are scalable17,18 but limited to pairwise gates19,20,21,22,23. Here we propose and implement a scalable scheme for realizing global entangling gates on multiple 171Yb+ ion qubits by coupling to multiple motional modes through modulated laser fields. Because such global gates require decoupling multiple modes and balancing all pairwise coupling strengths during the gate, we develop a system with fully independent control capability on each ion14. To demonstrate the usefulness and flexibility of these global gates, we generate a Greenberger–Horne–Zeilinger state with up to four qubits using a single global operation. Our approach realizes global entangling gates as scalable building blocks for universal quantum computation, motivating future research in scalable global methods for quantum information processing.

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Fig. 1: Global entangling gate and its experimental implementation.
Fig. 2: Experimental implementation of a global three-qubit entangling gate.
Fig. 3: Experimental implementation and results of the global entangling gates in three-ion qubits.
Fig. 4: Experimental implementation and results of the global entangling gate in a four-ion system.

Data availability

All relevant data are available from the corresponding authors upon request.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China under grants 2016YFA0301900 and 2016YFA0301901 and the National Natural Science Foundation of China under grants 11574002 and 11504197.

Reviewer information

Nature thanks Chris Ballance, Roee Ozeri and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Author information

Y.L., S.Z., K.Z., W.C. and Y.S. developed the experimental system. Y.L. and K.Z., together with J.-N.Z., investigated the theoretical schemes and optimized the pulse sequences. Y.L. and S.Z. obtained the data. K.K. supervised the project. Y.L. led the writing of the manuscript, with contributions from all authors.

Correspondence to Yao Lu or Kihwan Kim.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Comparison between gate durations of single- and multi-mode approaches.

For the given trap frequencies, the gate duration τ of the single-mode approach grows faster than linearly (τ ≈ N2.4) to maintain the fidelity F when the number of ions, N, increases. The gate duration of the multi-mode approach grows near linearly, with a theoretical fidelity of unity. The vertical axis is on a logarithmic scale.

Extended Data Fig. 2 Side view of the experimental ion-trap system.

The figure shows the structure of the blade trap. The radiofrequency potential is applied to the RF electrodes and the direct-current (DC) electrodes are connected to the direct-current potential. A static magnetic field of B ≈ 6 × 10−4 T is applied along the direction shown in the figure. The cover-all beam goes through the side viewport and is focused at the ion-chain position into an elliptical Gaussian beam, with waists of about 30 μm along the ion chain and about 5 μm in the perpendicular direction. The individual beams go through the bottom re-entry viewport and have a focused radius of about 1 μm at the ion position. The average laser power is around 120 mW for the cover-all beam and around 1 mW for each individual beam. The effective wave vector Δk of the two Raman beams is almost in the x direction, and the beams are polarized linearly, perpendicular to each other.

Extended Data Fig. 3 Motional trajectories in phase space for the global four-qubit entangling gate.

Because we apply different modulated-phase patterns to the qubits (1, 4) and (2, 3), the shapes of the motional trajectories in ad and eh are different.

Extended Data Table 1 Pulse scheme for the global three-qubit entangling gate
Extended Data Table 2 Pulse scheme for the global four-qubit entangling gate

Supplementary information

Supplementary Information

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