High-dimensional one-way quantum processing implemented on d-level cluster states


Taking advantage of quantum mechanics for executing computational tasks faster than classical computers1 or performing measurements with precision exceeding the classical limit2,3 requires the generation of specific large and complex quantum states. In this context, cluster states4 are particularly interesting because they can enable the realization of universal quantum computers by means of a ‘one-way’ scheme5, where processing is performed through measurements6. The generation of cluster states based on sub-systems that have more than two dimensions, d-level cluster states, provides increased quantum resources while keeping the number of parties constant7, and also enables novel algorithms8. Here, we experimentally realize, characterize and test the noise sensitivity of three-level, four-partite cluster states formed by two photons in the time9 and frequency10 domain, confirming genuine multi-partite entanglement with higher noise robustness compared to conventional two-level cluster states6,11,12,13. We perform proof-of-concept high-dimensional one-way quantum operations, where the cluster states are transformed into orthogonal, maximally entangled d-level two-partite states by means of projection measurements. Our scalable approach is based on integrated photonic chips9,10 and optical fibre communication components, thus achieving new and deterministic functionalities.

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Fig. 1: Time-frequency hyper-entanglement scheme.
Fig. 2: Generation of d-level cluster states with a controlled phase gate.
Fig. 3: Experimental demonstration of cluster state generation and related noise characteristics.
Fig. 4: High-dimensional one-way computation operations by measurement-based generation of orthogonal d-level two-party entangled quantum states.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Steacie, Strategic, Discovery and Acceleration Grants Schemes, by the MESI PSR-SIIRI Initiative in Quebec, by the Canada Research Chair Program and by the Australian Research Council Discovery Projects scheme (DP150104327). C.R., P.R. and S.L. acknowledge the support of NSERC Vanier Canada Graduate Scholarships. M.K. acknowledges funding from the European Union’s Horizon 2020 Research and Innovation programme under the Marie Sklodowska-Curie grant agreement number 656607. S.T.C. acknowledges support from the CityU APRC programme number 9610356. B.E.L. acknowledges support from the Strategic Priority Research Program of the Chinese Academy of Sciences (grant number XDB24030300). W.J.M. acknowledges support from the John Templeton Foundation (JTF) number 60478. R.M. acknowledges additional support by the Government of the Russian Federation through the ITMO Fellowship and Professorship Program (grant 074-U 01) and from the 1000 Talents Sichuan Program. We thank R. Helsten for technical insights; A. Tavares and K. Nemoto for discussions; P. Kung from QPS Photronics for help and the use of processing equipment; and Quantum Opus and N. Bertone of OptoElectronics Components for their support and for providing us with state-of-the-art photon detection equipment.

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C.R. and M.K. contributed equally. M.K., C.R., P.R., and S.S. developed the idea. C.R., M.K. P.R., M.I., Y.Z., L.R.C., and B.F. performed the measurements and analyzed the data. S.S., C.R., M.K., L.C., and W.J.M. performed the theoretical analysis. S.T.C. and B.E.L. designed and fabricated the microring resonator. S.L. and R.K. designed and fabricated the fibre Bragg gratings. D.J.M. and A.C. contributed to discussions. R.M. and J.A. managed the project. All authors contributed to the writing of the manuscript.

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Correspondence to Michael Kues or Roberto Morandotti.

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Reimer, C., Sciara, S., Roztocki, P. et al. High-dimensional one-way quantum processing implemented on d-level cluster states. Nature Phys 15, 148–153 (2019). https://doi.org/10.1038/s41567-018-0347-x

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