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Demonstration of three- and four-body interactions between trapped-ion spins

Nature Physics volume 19, pages 1452–1458 (2023)Cite this article

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Abstract

Quantum processors use the native interactions between effective spins to simulate Hamiltonians or execute quantum gates. In most processors, the native interactions are pairwise, limiting the efficiency of controlling entanglement between many qubits. The capability of manipulating entanglement generated by higher-order interactions is a key challenge for the simulation of many Hamiltonian models appearing in various fields, including high-energy and nuclear physics, as well as quantum chemistry and error correction applications. Here we experimentally demonstrate control over a class of native interactions between trapped-ion qubits, extending conventional pairwise interactions to a higher order. By exploiting state-dependent squeezing operations, we realize and characterize high-fidelity gates and spin Hamiltonians comprising three- and four-body spin interactions. Our results demonstrate the potential of high-order spin interactions as a toolbox for quantum information applications.

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Fig. 1: Native operations of a trapped-ion quantum processor.
Fig. 2: Quantum phase gates.
Fig. 3: Characterization of a three-body interaction gate.
Fig. 4: Evolution by effective Hamiltonians with three- and four-body interactions.

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Source data are provided with this paper. Other data that support the findings of this study are available from the corresponding authors on reasonable request.

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Acknowledgements

We thank A. Schuckert for useful comments. This work is supported by the ARO through the IARPA LogiQ program; the NSF STAQ and QLCI programs; the DOE QSA program; the AFOSR MURIs on Dissipation Engineering in Open Quantum Systems, Quantum Measurement/Verification and Quantum Interactive Protocols; the ARO MURI on Modular Quantum Circuits; and the DOE HEP QuantISED Program.

Author information

Authors and Affiliations

  1. Duke Quantum Center, Duke University, Durham, NC, USA

    Or Katz, Lei Feng, Christopher Monroe & Marko Cetina

  2. Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

    Or Katz, Lei Feng, Christopher Monroe & Marko Cetina

  3. Department of Physics, Duke University, Durham, NC, USA

    Or Katz, Lei Feng, Christopher Monroe & Marko Cetina

  4. Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA

    Andrew Risinger

  5. IonQ, Inc., College Park, MD, USA

    Christopher Monroe

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  1. Or Katz
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Contributions

All authors contributed to the experimental design, construction and discussions and wrote the manuscript. O.K. collected the data, and O.K. and L.F. analysed the results. L.F. produced Fig. 1. O.K. produced Figs. 2–4.

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Correspondence to Or Katz or Lei Feng.

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Competing interests

O.K., L.F. and A.R. declare that they have no competing interests. M.C. is a co-inventor of the intellectual property that is licensed by the University of Maryland to IonQ, Inc. C.M. is a co-founder and chief scientist at IonQ, Inc.

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Nature Physics thanks Christian Schmiegelow and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Experimental sequences.

a, Sequence of displacement operations acting on the two edge ions and composing the MS interaction, enclosing a closed rectangular loop in phase-space and generating the evolution in Fig. 2a. b, Superimposing spin-dependent squeezing operations on the second spin scales the displacement generated by the third spin by a factor \(\exp ({\hat{\sigma }}_{x}^{(2)}\xi )\) and consequently also the enclosed phase-space area. This sequence was applied to the configurations in Fig. 2b–c and in Fig. 3 and Fig. 4a. c, Displacement of the edge two spins and simultaneous squeezing of the middle spins for the four ions configuration presented in Fig. 4b. The simultaneous squeezing scales the displacement generated by the fourth spin by a spin-dependent factor \(\exp ({\hat{\sigma }}_{x}^{(2)}\xi +{\hat{\sigma }}_{x}^{(3)}\zeta\,\, )\) as seen from the identity \({S}^{(m)}(-\xi ){D}_{p}^{(n)}(\pm \alpha ){S}^{(m)}(\xi )={D}_{p}^{(n)}(\pm {e}^{{\hat{\sigma }}_{x}^{(m)}\xi }\alpha )\). The operators \({D}_{p}^{(n)}(\pm \alpha )\) and \({D}_{q}^{(n)}(\pm \alpha )\) denote displacement of the target phonon mode via the nth ion by ± α along the p and q coordinates respectively. S(m)( ± ξ) denotes the squeezing operator acting on ion m and \({R}_{\theta }^{(n)}(\pm \pi )\) denotes short single-qubit π-pulses acting on the n th ion, which commute with the spin-dependent displacement operations and which correct for slowly-varying uncompensated Stark shifts without altering the target state. See Methods for further details.

Supplementary information

Supplementary Information

Supplementary Note 1 and Figs. 1–4.

Source data

Source Data Fig. 2

Data for Fig. 2a–c.

Source Data Fig. 3

Data for Fig. 3a,b.

Source Data Fig. 4

Data for Fig. 4a,b.

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Katz, O., Feng, L., Risinger, A. et al. Demonstration of three- and four-body interactions between trapped-ion spins. Nat. Phys. 19, 1452–1458 (2023). https://doi.org/10.1038/s41567-023-02102-7

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