Fast quantum logic gates with trapped-ion qubits


Quantum bits (qubits) based on individual trapped atomic ions are a promising technology for building a quantum computer1. The elementary operations necessary to do so have been achieved with the required precision for some error-correction schemes2,3,4. However, the essential two-qubit logic gate that is used to generate quantum entanglement has hitherto always been performed in an adiabatic regime (in which the gate is slow compared with the characteristic motional frequencies of the ions in the trap3,4,5,6,7), resulting in logic speeds of the order of 10 kilohertz. There have been numerous proposals of methods for performing gates faster than this natural ‘speed limit’ of the trap8,9,10,11,12. Here we implement one such method11, which uses amplitude-shaped laser pulses to drive the motion of the ions along trajectories designed so that the gate operation is insensitive to the optical phase of the pulses. This enables fast (megahertz-rate) quantum logic that is robust to fluctuations in the optical phase, which would otherwise be an important source of experimental error. We demonstrate entanglement generation for gate times as short as 480 nanoseconds—less than a single oscillation period of an ion in the trap and eight orders of magnitude shorter than the memory coherence time measured in similar calcium-43 hyperfine qubits. The power of the method is most evident at intermediate timescales, at which it yields a gate error more than ten times lower than can be attained using conventional techniques; for example, we achieve a 1.6-microsecond-duration gate with a fidelity of 99.8 per cent. Faster and higher-fidelity gates are possible at the cost of greater laser intensity. The method requires only a single amplitude-shaped pulse and one pair of beams derived from a continuous-wave laser. It offers the prospect of combining the unrivalled coherence properties2,13, operation fidelities2,3,4 and optical connectivity14 of trapped-ion qubits with the submicrosecond logic speeds that are usually associated with solid-state devices15,16.

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Figure 1: Qubit states and Raman beam geometry.
Figure 2: Optical beat notes and motional trajectories of the ions for two initial optical phases (ϕ0 = 0 and ϕ0 = π/2).
Figure 3: Theoretical and experimental two-qubit gate errors.


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This work was supported by the UK EPSRC ‘Networked Quantum Information Technologies’ Hub, and the UK Defence, Science and Technology Laboratory. V.M.S. acknowledges funding from Balliol College, Oxford. C.J.B. acknowledges funding from Magdalen College, Oxford. We thank S. R. Woodrow for work on the trap design, T. P. Harty for contributions to the apparatus and W. Zhang for the loan of the AWG. We acknowledge the use of the University of Oxford Advanced Research Computing facility ( The experiments benefitted from the use of the ARTIQ control system (

Author information

C.J.B. performed the numerical modelling. V.M.S. and C.J.B. designed and performed the experiments and analysed the data. K.T. built the ion trap and characterized the fast AOMs. L.J.S. and T.G.B. built optical and control systems. V.M.S., C.J.B., A.M.S. and D.M.L. wrote the manuscript, which all authors discussed.

Correspondence to D. M. Lucas.

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Extended data figures and tables

Extended Data Table 1 Gate parameters used for the fastest gate (seven segments) and for the highest-fidelity gate (five segments)

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Schäfer, V., Ballance, C., Thirumalai, K. et al. Fast quantum logic gates with trapped-ion qubits. Nature 555, 75–78 (2018).

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