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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References
Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2010).
Casanova, J., Mezzacapo, A., Lamata, L. & Solano, E. Quantum simulation of interacting fermion lattice models in trapped ions. Phys. Rev. Lett. 108, 190502 (2012).
Yung, M.-H. et al. From transistor to trapped-ion computers for quantum chemistry. Sci. Rep. 4, 3589 (2015).
Ivanov, S. S., Ivanov, P. A. & Vitanov, N. V. Efficient construction of three- and four-qubit quantum gates by global entangling gates. Phys. Rev. A 91, 032311 (2015).
Martinez, E. A., Monz, T., Nigg, D., Schindler, P. & Blatt, R. Compiling quantum algorithms for architectures with multi-qubit gates. New J. Phys. 18, 063029 (2016).
Maslov, D. & Nam, Y. Use of global interactions in efficient quantum circuit constructions. New J. Phys. 20, 033018 (2018).
Kim, K. et al. Entanglement and tunable spin–spin couplings between trapped ions using multiple transverse modes. Phys. Rev. Lett. 103, 120502 (2009).
Britton, J. W. et al. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012).
Senko, C. et al. Coherent imaging spectroscopy of a quantum many-body spin system. Science 345, 430–433 (2014).
Jurcevic, P. et al. Spectroscopy of interacting quasiparticles in trapped ions. Phys. Rev. Lett. 115, 100501 (2015).
Debnath, S. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016).
Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).
Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).
García-Ripoll, J. J., Zoller, P. & Cirac, J. I. Coherent control of trapped ions using off-resonant lasers. Phys. Rev. A 71, 062309 (2005).
Zhu, S.-L., Monroe, C. & Duan, L.-M. Trapped ion quantum computation with transverse phonon modes. Phys. Rev. Lett. 97, 050505 (2006).
Steane, A. M., Imreh, G., Home, J. P. & Leibfried, D. Pulsed force sequences for fast phase-insensitive quantum gates in trapped ions. New J. Phys. 16, 053049 (2014).
Choi, T. et al. Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement. Phys. Rev. Lett. 112, 190502 (2014).
Leung, P. H. et al. Robust 2-qubit gates in a linear ion crystal using a frequency-modulated driving force. Phys. Rev. Lett. 120, 020501 (2018).
Milne, A. R. et al. Phase-modulated entangling gates robust against static and time-varying errors. Preprint at https://arxiv.org/abs/1808.10462 (2018).
Schäfer, V. M. et al. Fast quantum logic gates with trapped-ion qubits. Nature 555, 75–78 (2018).
Kaufmann, H. et al. Scalable creation of long-lived multipartite entanglement. Phys. Rev. Lett. 119, 150503 (2017).
Haljan, P. C., Brickman, K.-A., Deslauriers, L., Lee, P. J. & Monroe, C. Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion. Phys. Rev. Lett. 94, 153602 (2005).
Lechner, R. et al. Electromagnetically-induced-transparency ground-state cooling of long ion strings. Phys. Rev. A 93, 053401 (2016).
Webb, A. E. et al. Resilient entangling gates for trapped ions. Phys. Rev. Lett. 121, 180501 (2018).
Shapira, Y., Shaniv, R., Manovitz, T., Akerman, N. & Ozeri, R. Robust entanglement gates for trapped-ion qubits. Phys. Rev. Lett. 121, 180502 (2018).
Roos, C. F. Ion trap quantum gates with amplitude-modulated laser beams. New J. Phys. 10, 013002 (2008).
Olmschenk, S. et al. Manipulation and detection of a trapped Yb+ hyperfine qubit. Phys. Rev. A 76, 052314 (2007).
Hayes, D. et al. Entanglement of atomic qubits using an optical frequency comb. Phys. Rev. Lett. 104, 140501 (2010).
Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000).
Figgatt, C. et al. Parallel entangling operations on a universal ion trap quantum computer. Nature https://doi.org/10.1038/s41586-019-1427-5 (2019).
Duan, L.-M. & Shen, C. Correcting detection errors in quantum state engineering through data processing. New J. Phys. 14, 1778–1782 (2012).
Richerme, P. et al. Non-local propagation of correlations in quantum systems with long-range interactions. Nature 511, 198–201 (2014).
James, D. F. V. Quantum dynamics of cold trapped ions with application to quantum computation. Appl. Phys. B 66, 181–190 (1998).
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.
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Nature thanks Chris Ballance, Roee Ozeri and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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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.
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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 a–d and e–h are different.
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Lu, Y., Zhang, S., Zhang, K. et al. Global entangling gates on arbitrary ion qubits. Nature 572, 363–367 (2019). https://doi.org/10.1038/s41586-019-1428-4
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DOI: https://doi.org/10.1038/s41586-019-1428-4
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