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Scalable and programmable phononic network with trapped ions

Nature Physics volume 19, pages 877–883 (2023)Cite this article

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Abstract

A network of bosons evolving among different modes while passing through beam splitters and phase shifters has been applied to demonstrate quantum computational advantage. While such networks have mostly been implemented in optical systems using photons, alternative realizations addressing major limitations in photonic systems such as photon loss have been explored recently. Quantized excitations of vibrational modes (phonons) of trapped ions are a promising candidate to realize such bosonic networks. Here, we demonstrate a minimal-loss programmable phononic network in which any phononic state can be deterministically prepared and detected. We realize networks with up to four collective vibrational modes, which can be extended to reveal quantum advantage. We benchmark the performance of the network for an exemplary tomography algorithm using arbitrary multi-mode states with fixed total phonon number. We obtain high reconstruction fidelities for both single- and two-phonon states. Our experiment demonstrates a clear pathway to scale up a phononic network for quantum information processing beyond the limitations of classical and photonic systems.

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Fig. 1: Overview of the phononic network.
Fig. 2: Beam splitters.
Fig. 3: Tomography experiment with single phonon.
Fig. 4: Tomography experiment with two phonons.

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Data availability

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

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Acknowledgements

This work was supported by the innovation Program for Quantum Science and Technology under grant no. 2021ZD0301602, the National Key Research and Development Program of China under grant nos. 2016YFA0301900 and 2016YFA0301901, the National Natural Science Foundation of China grant nos. 92065205 and 11974200. M.S.K.’s work was supported by the UK Hub in Quantum Computing and Simulation, part of the UK National Quantum Technologies Programme with funding from UKRI EPSRC grant EP/T001062/1 and by the Korea Institute of Science and Technology (KIST) Open Research Program. L.B. acknowledges support from the Rita Levi Montalcini program for young researchers. We thank L. You for carefully reading of the manuscript.

Author information

Authors and Affiliations

  1. State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, P. R. China

    Wentao Chen, Yao Lu, Shuaining Zhang, Kuan Zhang, Guanhao Huang, Mu Qiao, Xiaolu Su, Jialiang Zhang & Kihwan Kim

  2. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, P. R. China

    Yao Lu

  3. Department of Physics, Renmin University of China, Beijing, China

    Shuaining Zhang

  4. MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF, Institute for Quantum Science and Engineering, School of Physics, Huazhong University of Science and Technology, Wuhan, P. R. China

    Kuan Zhang

  5. Beijing Academy of Quantum Information Sciences, Beijing, P. R. China

    Jing-Ning Zhang & Kihwan Kim

  6. Dipartimento di Fisica e Astronomia, Università di Firenze, Sesto Fiorentino, Italy

    Leonardo Banchi

  7. INFN, Sezione di Firenze, Sesto Fiorentino, Italy

    Leonardo Banchi

  8. QOLS, Blackett Laboratory, Imperial College London, London, UK

    M. S. Kim

  9. Hefei National Laboratory, Hefei, P. R. China

    Kihwan Kim

  10. Frontier Science Center for Quantum Information, Beijing, P. R. China

    Kihwan Kim

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  1. Wentao Chen
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Contributions

W.C., Y.L., S.Z. and K.Z. developed the experimental system with assistance from X.S. and J.Z.. L.B. and M.S.K. provided the theoretical idea, and W.C., Y.L. and J.-N.Z. optimized experimental schemes with help from G.H. and M.Q. W.C. took and analysed the data. K.K. supervised the project. W.C., L.B., M.S.K. and K.K. contributed to the writing of the manuscript with the agreement of all the other authors.

Corresponding authors

Correspondence to Wentao Chen, M. S. Kim or Kihwan Kim.

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Extended data

Extended Data Fig. 1 Imaging system for the fluorescence detection of individual ion-qubit states.

The fluorescence of five ions is collected by a high NA lens and imaged to 32-channel PMT. To reduce crosstalk, we image each ion into alternative channels of PMT and put a slit at the second focused plane of the imaging system to suppress horizontal and vertical components, respectively.

Extended Data Fig. 2 Raman schematic diagram of beam-splitter.

a, Frequency arrangement of two Raman lasers from perpendicular directions. Raman I is a global laser with one frequency component, and Raman II is an individually addressed laser with two components focused on one ion. b, Energy diagram of beam-splitter. Δbs is a frequency detuning between Raman I and Raman II, effectively introducing two off-resonant RSB on a single ion. ω0 is the frequency of ion-qubit. Here two energy levels are connected by the Raman transition, \(\left| \downarrow \right\rangle _i\left| 1 \right\rangle _1\left| 0 \right\rangle _2\) and \(\left| \downarrow \right\rangle _i\left| 0 \right\rangle _1\left| 1 \right\rangle _2\).

Extended Data Fig. 3 Raman schematic diagram of beam-splitter.

a, Fidelity of a 50:50 beam-splitter with \(R_1 = {{\Delta }}_{{{{\mathrm{bs}}}}}/\sqrt {{{{\mathrm{\eta }}}}_{j,m}{{\Omega }}_{j,m}{{{\mathrm{\eta }}}}_{j,n}{{\Omega }}_{j,n}}\) and \(R_2 = {{{\mathrm{\delta }}}}\overline {{{{\mathrm{\nu }}}}_M} /{{\Delta }}_{{{{\mathrm{bs}}}}}\), where ηj,m and ηj,n are Lamb-Dicke parameters of two modes and Ωj,m is the Rabi frequency of frequency component \(f_{j,m} - f_0\). b, Prediction of operation time for a 50:50 beam-splitter. Here the simulation based on an average mode spacing of 50 kHz.

Extended Data Fig. 4 Numerical simulation for systematic errors of beam-splitters.

We simulate the performance of 50:50 beam-splitters with similar parameters used in the experiment. We achieve population errors induced by (a) heating, (b) motional decoherence, and (c) spin decoherence by subtracting inevitable errors caused by off-resonant couplings shown in Extended Data Fig. 3a. The blue points represent simulation results, with the orange fitting curves representing the error trend. The green stars represent the measurement results of the corresponding values.

Extended Data Fig. 5 Fidelity measurements of beam-splitters.

We calculate the population fidelity of beam-splitters between modes (a) 1 and 2, (b) 2 and 4, (c) 1 and 3, (d) 3 and 4, using data shown in Fig. 2. The blue circles represent the calculated fidelity, and the blue dashed lines represent the linear fitting results. The intersection of the blue and red lines represents the fidelities of the 50:50 beam splitters. All the data points occur in the figures were obtained from the mean value of 100 samples, and the error bars represent 95% confidence intervals.

Extended Data Table 1 Detection and preparation fidelities of each mode
Full size table
Extended Data Table 2 Parameters and fidelities of 50:50 beam-splitters in four-mode setup
Full size table
Extended Data Table 3 Reconstruction results for two modes input states without using ancillary modes
Full size table
Extended Data Table 4 Interferometric configuration for a two-mode input state with two ancillary modes
Full size table
Extended Data Table 5 Reconstruction results for two modes input states using two ancillary modes
Full size table

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and discussion.

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Chen, W., Lu, Y., Zhang, S. et al. Scalable and programmable phononic network with trapped ions. Nat. Phys. 19, 877–883 (2023). https://doi.org/10.1038/s41567-023-01952-5

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