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Error-protected qubits in a silicon photonic chip

Nature Physics volume 17, pages 1137–1143 (2021)Cite this article

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Abstract

General-purpose quantum computers can, in principle, entangle a number of noisy physical qubits to realize composite qubits protected against errors. Architectures for measurement-based quantum computing intrinsically support error-protected qubits and are the most viable approach for constructing an all-photonic quantum computer. Here we propose and demonstrate an integrated silicon photonic scheme that both entangles multiple photons, and encodes multiple physical qubits on individual photons, to produce error-protected qubits. We realize reconfigurable graph states to compare several schemes with and without error-correction encodings and implement a range of quantum information processing tasks. We observe a success rate increase from 62.5% to 95.8% when running a phase-estimation algorithm without and with error protection, respectively. Finally, we realize hypergraph states, which are a generalized class of resource states that offer protection against correlated errors. Our results show how quantum error-correction encodings can be implemented with resource-efficient photonic architectures to improve the performance of quantum algorithms.

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Fig. 1: Device description and performance.
Fig. 2: Graph state fidelities.
Fig. 3: MBQC operations with physical and logical graph states.
Fig. 4: Experimental results for MBQC PEA with physical and logical graphs.
Fig. 5: Results for MBQC with hypergraphs.

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Data availability

The data that support the plots within this paper and other findings of this study are available at https://doi.org/10.6084/m9.figshare.11903427.

References

  1. Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).

    Article  ADS  Google Scholar 

  2. Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579 (2017).

    Article  ADS  Google Scholar 

  3. Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

    Article  Google Scholar 

  4. Gottesman, D. Stabilizer Codes and Quantum Error Correction. PhD thesis, Californian Institute of Technology (1997).

  5. Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error rate. Preprint at https://arxiv.org/abs/quant-ph/9906129 (1999).

  6. Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001).

    Article  ADS  Google Scholar 

  7. Raussendorf, R., Browne, D. E. & Briegel, H. J. Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312 (2003).

    Article  ADS  Google Scholar 

  8. Walther, P. et al. Experimental one-way quantum computing. Nature 434, 169 (2005).

    Article  ADS  Google Scholar 

  9. Vallone, G., Pomarico, E., De Martini, F. & Mataloni, P. Active one-way quantum computation with two-photon four-qubit cluster states. Phys. Rev. Lett. 100, 160502 (2008).

    Article  ADS  Google Scholar 

  10. Wang, Y., Li, Y., Yin, Z. & Zeng, B. 16-qubit IBM universal quantum computer can be fully entangled. npj Quantum Inf. 4, 1 (2018).

    Article  ADS  Google Scholar 

  11. Zwerger, M., Briegel, H. J. & Dür, W. Hybrid architecture for encoded measurement-based quantum computation. Sci. Rep. 4, 5364 (2014).

    Article  ADS  Google Scholar 

  12. Raussendorf, R., Harrington, J. & Goyal, K. Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9, 199 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  13. Schlingemann, D. & Werner, R. F. Quantum error-correcting codes associated with graphs. Phys. Rev. A 65, 012308 (2001).

    Article  ADS  Google Scholar 

  14. Lanyon, B. P. et al. Measurement-based quantum computation with trapped ions. Phys. Rev. Lett. 111, 210501 (2013).

    Article  ADS  Google Scholar 

  15. Barz, S. et al. Demonstrating elements of measurement-based quantum error correction. Phys. Rev. A 90, 042302 (2014).

    Article  ADS  Google Scholar 

  16. Yao, X.-C. et al. Experimental demonstration of topological error correction. Nature 482, 489 (2012).

    Article  ADS  Google Scholar 

  17. Bell, B. et al. Experimental demonstration of a graph state quantum error-correction code. Nat. Commun. 5, 1 (2014).

    ADS  Google Scholar 

  18. Varnava, M., Browne, D. E. & Rudolph, T. How good must single photon sources and detectors be for efficient linear optical quantum computation? Phys. Rev. Lett. 100, 060502 (2008).

    Article  ADS  Google Scholar 

  19. Gimeno-Segovia, M., Shadbolt, P., Browne, D. E. & Rudolph, T. From three-photon Greenberger–Horne–Zeilinger states to ballistic universal quantum computation. Phys. Rev. Lett. 115, 020502 (2015).

    Article  ADS  Google Scholar 

  20. Rudolph, T. Why I am optimistic about the silicon-photonic route to quantum computing. APL Photon. 2, 030901 (2017).

    Article  ADS  Google Scholar 

  21. Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Harris, N. C. et al. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photon. 11, 447 (2017).

    Article  ADS  Google Scholar 

  23. Adcock, J. C., Vigliar, C., Santagati, R., Silverstone, J. W. & Thompson, M. G. Programmable four-photon graph states on a silicon chip. Nat. Commun. 10, 3528 (2019).

    Article  ADS  Google Scholar 

  24. Llewellyn, D. et al. Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys. 16, 1 (2019).

    Google Scholar 

  25. Barreiro, J. T., Langford, N. K., Peters, N. A. & Kwiat, P. G. Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005).

    Article  ADS  Google Scholar 

  26. Vallone, G., Pomarico, E., Mataloni, P., De Martini, F. & Berardi, V. Realization and characterization of a two-photon four-qubit linear cluster state. Phys. Rev. Lett. 98, 180502 (2007).

    Article  ADS  Google Scholar 

  27. Reimer, C. et al. High-dimensional one-way quantum processing implemented on d-level cluster states. Nat. Phys. 15, 148 (2019).

    Article  Google Scholar 

  28. Zhang, Q. et al. Demonstration of a scheme for the generation of ‘event-ready’ entangled photon pairs from a single-photon source. Phys. Rev. A 77, 062316 (2008).

    Article  ADS  Google Scholar 

  29. Ding, Y., Peucheret, C., Ou, H. & Yvind, K. Fully etched apodized grating coupler on the SOI platform with −0.58 db coupling efficiency. Opt. Lett. 39, 5348 (2014).

    Article  ADS  Google Scholar 

  30. Malik, M. et al. Multi-photon entanglement in high dimensions. Nat. Photon. 10, 248 (2016).

    Article  ADS  Google Scholar 

  31. Adcock, J. C., Morley-Short, S., Silverstone, J. W. & Thompson, M. G. Hard limits on the postselectability of optical graph states. Quantum Sci. Technol. 4, 015010 (2018).

    Article  ADS  Google Scholar 

  32. Gu, X., Erhard, M., Zeilinger, A. & Krenn, M. Quantum experiments and graphs II: quantum interference, computation, and state generation. Proc. Natl Acad. Sci. USA 116, 4147 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Gühne, O. & Tóth, G. Entanglement detection. Phys. Rep. 474, 1 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  34. Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S. & Eisert, J. Quantum state tomography via compressed sensing. Phys. Rev. Lett. 105, 150401 (2010).

    Article  ADS  Google Scholar 

  35. Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256 (2000).

    Article  ADS  Google Scholar 

  36. Wang, X.-L. et al. Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016).

    Article  ADS  Google Scholar 

  37. Hein, M., Eisert, J. & Briegel, H. J. Multiparty entanglement in graph states. Phys. Rev. A 69, 062311 (2004).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Nielsen, M. A. & Chuang, I. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2002).

  39. Morley-Short, S., Gimeno-Segovia, M., Rudolph, T. & Cable, H. Loss-tolerant teleportation on large stabilizer states. Quantum Sci. Technol. 4, 025014 (2019).

    Article  ADS  Google Scholar 

  40. Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059 (2011).

    Article  ADS  Google Scholar 

  41. O’Malley, P. J. J. et al. Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016).

    Google Scholar 

  42. Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M. & Pryde, G. J. Entanglement-free Heisenberg-limited phase estimation. Nature 450, 393 (2007).

    Article  ADS  Google Scholar 

  43. Friis, N. et al. Flexible resources for quantum metrology. New J. Phys. 19, 063044 (2017).

    Article  ADS  Google Scholar 

  44. Paesani, S. et al. Experimental Bayesian quantum phase estimation on a silicon photonic chip. Phys. Rev. Lett. 118, 100503 (2017).

    Article  ADS  Google Scholar 

  45. Dobšíček, M., Johansson, G., Shumeiko, V. & Wendin, G. Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: a two-qubit benchmark. Phys. Rev. A 76, 030306 (2007).

    Article  ADS  Google Scholar 

  46. Kitaev, A. Y. Quantum measurements and the Abelian stabilizer problem. Preprint at https://arxiv.org/abs/quant-ph/9511026 (1995).

  47. Qu, R., Wang, J., Li, Z.-S. & Bao, Y.-R. Encoding hypergraphs into quantum states. Phys. Rev. A 87, 022311 (2013).

    Article  ADS  Google Scholar 

  48. Rossi, M., Huber, M., Bruß, D. & Macchiavello, C. Quantum hypergraph states. New J. Phys. 15, 113022 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. Gühne, O. et al. Entanglement and nonclassical properties of hypergraph states. J. Phys. A 47, 335303 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  50. Miller, J. & Miyake, A. Hierarchy of universal entanglement in 2D measurement-based quantum computation. npj Quantum Inf. 2, 16036 (2016).

    Article  ADS  Google Scholar 

  51. Gachechiladze, M., Budroni, C. & Gühne, O. Extreme violation of local realism in quantum hypergraph states. Phys. Rev. Lett. 116, 070401 (2016).

    Article  ADS  Google Scholar 

  52. Gachechiladze, M., Gühne, O. & Miyake, A. Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states. Phys. Rev. A 99, 052304 (2019).

    Article  ADS  Google Scholar 

  53. Lyons, D. W. et al. Local Pauli stabilizers of symmetric hypergraph states. J. Phys. A 50, 245303 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. Gachechiladze, M., Tsimakuridze, N. & Gühne, O. Graphical description of unitary transformations on hypergraph states. J. Phys. A 50, 19LT01 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  55. Morimae, T., Takeuchi, Y. & Hayashi, M. Verification of hypergraph states. Phys. Rev. A 96, 062321 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  56. LoPiparo, N., Hanks, M., Gravel, C., Nemoto, K. & Munro, W. J. Resource reduction for distributed quantum information processing using quantum multiplexed photons. Phys. Rev. Lett. 124, 210503 (2020).

    Article  ADS  Google Scholar 

  57. Wang, H. et al. Towards optimal single-photon sources from polarized microcavities. Nat. Photon. 13, 770 (2019).

    Article  ADS  Google Scholar 

  58. Paesani, S. et al. Near-ideal spontaneous photon sources in silicon quantum photonics. Nat. Commun. 11, 1 (2020).

    Article  Google Scholar 

  59. Eltes, F. et al. An integrated cryogenic optical modulator. Preprint at https://arxiv.org/abs/1904.10902 (2019).

  60. Atabaki, A. H. et al. Integrating photonics with silicon nanoelectronics for the next generation of systems on a chip. Nature 556, 349 (2018).

    Article  ADS  Google Scholar 

  61. Paesani, S. et al. Generation and sampling of quantum states of light in a silicon chip. Nat. Phys. 15, 925 (2019).

    Article  Google Scholar 

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Acknowledgements

We thank R. Santagati, A. E. Jones, J. F. Bulmer, R. Shaw, D. D. Roberts, J. F. Tasker, N. Maraviglia, J. W. Silverstone, W. A. Murray, Z. Raissi, C. Gogolin and P. Skrzypczyk for useful discussions and technical assistance. We acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC) and European Commission (EC) funded grants PICQUE, BBOI, QUCHIP, QuPIC, QITBOX, VILLUM FONDEN, QUANPIC (ref. 00025298), the Center of Excellence, Denmark SPOC (ref DNRF123) and ERA-NET cofund initiatives QuantERA within the European Union’s Horizon 2020 research and innovation programme grant agreement 731473 (project SQUARE). We acknowledge support from the EPSRC Hubs in Quantum Computing and Simulation (EP/T001062/1) and Networked Quantum Information Technologies (EP/N509711/1). Fellowship support from EPSRC is acknowledged by A.L. (EP/N003470/1).

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Authors and Affiliations

  1. Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol, UK

    Caterina Vigliar, Stefano Paesani, Jeremy C. Adcock, Sam Morley-Short, Mark G. Thompson, John G. Rarity & Anthony Laing

  2. Department of Photonics Engineering, Technical University of Denmark, Lyngby, Denmark

    Yunhong Ding, Davide Bacco & Leif K. Oxenløwe

  3. Center for Silicon Photonics for Optical Communication (SPOC), Technical University of Denmark, Lyngby, Denmark

    Yunhong Ding, Davide Bacco & Leif K. Oxenløwe

  4. State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China

    Jianwei Wang

  5. Frontiers Science Center for Nano-optoelectronics, Collaborative Innovation Center of Quantum Matter, Peking University, Bejing, China

    Jianwei Wang

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Contributions

C.V., S.P., Y.D., J.W., D.B., M.G.T. and A.L. designed the experiment. J.W. and S.P. designed the integrated circuit. Y.D. fabricated the silicon photonics device. C.V. and S.P. performed the experiment and analysed the data, with theoretical support from J.C.A. and S.M.-S. C.V., S.P., J.C.A. and A.L. wrote the manuscript with feedback from all authors. L.K.O., M.G.T., J.G.R. and A.L. managed the project.

Corresponding authors

Correspondence to Yunhong Ding, Jianwei Wang or Anthony Laing.

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Competing interests

M.G.T. is involved in developing quantum photonic technologies at PsiQuantum Corporation. The remaining authors declare no competing interests.

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Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary Sections 1–12, Figs. 1–16 and Tables 1–12.

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Vigliar, C., Paesani, S., Ding, Y. et al. Error-protected qubits in a silicon photonic chip. Nat. Phys. 17, 1137–1143 (2021). https://doi.org/10.1038/s41567-021-01333-w

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