Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Experimental validation of photonic boson sampling

Nature Photonics volume 8, pages 615–620 (2014)Cite this article

Subjects

Abstract

A boson sampling device is a specialized quantum computer that solves a problem that is strongly believed to be computationally hard for classical computers1. Recently, a number of small-scale implementations have been reported2,3,4,5, all based on multiphoton interference in multimode interferometers. Akin to several quantum simulation and computation tasks, an open problem in the hard-to-simulate regime is to what extent the correctness of the boson sampling outcomes can be certified6,7. Here, we report new boson sampling experiments on larger photonic chips and analyse the data using a recently proposed scalable statistical test8. We show that the test successfully validates small experimental data samples against the hypothesis that they are uniformly distributed. In addition, we show how to discriminate data arising from either indistinguishable or distinguishable photons. Our results pave the way towards larger boson sampling experiments whose functioning, despite being non-trivial to simulate, can be certified against alternative hypotheses.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Boson sampling and its certification.
Figure 2: Experimental validation of boson sampling.
Figure 3: Full validation of the boson sampling experiments.
Figure 4: Discrimination between alternative distributions.

Similar content being viewed by others

References

  1. Aaronson, S. & Arkhipov, A. in Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (eds Fortnow, L. & Vadhan, S.) 333–342 (ACM Press, 2011).

    MATH  Google Scholar 

  2. Crespi, A. et al. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nature Photon. 7, 545–549 (2013).

    Article  ADS  Google Scholar 

  3. Tillmann, M. et al. Experimental boson sampling. Nature Photon. 7, 540–544 (2013).

    Article  ADS  Google Scholar 

  4. Broome, M. A. et al. Photonic boson sampling in a tunable circuit. Science 339, 794–798 (2013).

    Article  ADS  Google Scholar 

  5. Spring, J. B. et al. Boson sampling on a photonic chip. Science 339, 798–801 (2013).

    Article  ADS  Google Scholar 

  6. Barz, S., Fitzsimons, J. F., Kashefi, E. & Walther, P. Experimental verification of quantum computation. Nature Phys. 9, 727–731 (2013).

    Article  ADS  Google Scholar 

  7. Gogolin, C., Kliesch, M., Aolita, L. & Eisert, J. Boson-sampling in the light of sample complexity. Preprint at http://lanl.arxiv.org/abs/1306.3995 (2013).

  8. Aaronson, S. & Arkhipov, A. Bosonsampling is far from uniform. Preprint at http://lanl.arxiv.org/abs/1309.7460 (2013).

  9. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).

    Article  MathSciNet  Google Scholar 

  10. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  ADS  Google Scholar 

  11. Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011).

    Article  ADS  Google Scholar 

  12. Islam, R. et al. Emergence and frustration of magnetism with variable-range interactions in a quantum simulator. Science 340, 583–587 (2013).

    Article  ADS  Google Scholar 

  13. Preskill, J. Quantum computing and the entanglement frontier. Preprint at http://lanl.arxiv.org/abs/1203.5813 (2012).

  14. Rohde, P. P. & Ralph, T. C. Error tolerance of the boson-sampling model for linear optics quantum computing. Phys. Rev. A 85, 022332 (2012).

    Article  ADS  Google Scholar 

  15. Leverrier, A. & García-Patrón, R. Does boson sampling need fault-tolerance? Preprint at http://lanl.arxiv.org/abs/1309.4687 (2013).

  16. Motes, K. R., Dowling, J. P. & Rohde, P. P. Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson-sampling. Phys. Rev. A 88, 063822 (2013).

    Article  ADS  Google Scholar 

  17. Rohde, P. P., Motes, K. R. & Dowling, J. P. Sampling generalized cat states with linear optics is probably hard. Preprint at http://lanl.arxiv.org/abs/1310.0297 (2013).

  18. Shen, C., Zhang, Z. & Duan, L.-M. Scalable implementation of boson sampling with trapped ions. Phys. Rev. Lett. 112, 050504 (2014).

    Article  ADS  Google Scholar 

  19. Davis, K. M., Miura, K., Sugimoto, N. & Hirao, K. Writing waveguides in glass with a femtosecond laser. Opt. Lett. 21, 1729–1731 (1996).

    Article  ADS  Google Scholar 

  20. Osellame, R. et al.Femtosecond writing of active optical waveguides with astigmatically shaped beams. J. Opt. Soc. Am. B 20, 1559–1567 (2003).

    Article  ADS  Google Scholar 

  21. Gattass, R. & Mazur, E. Femtosecond laser micromachining in transparent materials. Nature Photon. 2, 219–225 (2008).

    Article  ADS  Google Scholar 

  22. Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994).

    Article  ADS  Google Scholar 

  23. Sansoni, L. et al. Two-particle bosonic–fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012).

    Article  ADS  Google Scholar 

  24. Crespi, A. et al. Anderson localization of entangled photons in an integrated quantum walk. Nature Photon. 7, 322–328 (2013).

    Article  ADS  Google Scholar 

  25. Spagnolo, N. et al. Three-photon bosonic coalescence in an integrated tritter. Nature Commun. 4, 1606 (2013).

    Article  ADS  Google Scholar 

  26. Spagnolo, N. et al. General rules for bosonic bunching in multimode interferometers. Phys. Rev. Lett. 111, 130503 (2013).

    Article  ADS  Google Scholar 

  27. Cover, T. M. & Thomas, J. A. in Elements of Information Theory 2nd edn, Ch. 12 (Wiley-Interscience, 2006).

    MATH  Google Scholar 

  28. Tichy, M. C., Mayer, K., Buchleitner, A. & Mølmer, K. Stringent and efficient assessment of boson-sampling devices. Preprint at http://lanl.arxiv.org/abs/1312.3080 (2013).

  29. Carolan, J. et al. On the experimental verification of quantum complexity in linear optics. Preprint at http://lanl.arxiv.org/abs/1311.2913v2 (2013).

Download references

Acknowledgements

The authors acknowledge feedback from S. Aaronson, A. Arkhipov, L. Aolita and J. Eisert. This work was supported by the European Research Council (ERC-Starting Grant 3D-QUEST, 3D-Quantum Integrated Optical Simulation, grant agreement no. 307783, http://www.3dquest.eu/), by Progetto d'Ateneo SUPERCONTINUUM (Generation and Characterization of Supercontinuum Laser Sources for Bio-spectroscopy and Quantum Optics), by PRIN (Programmi di ricerca di rilevante interesse nazionale) project AQUASIM (Advanced Quantum Simulation and Metrology) and by the Brazilian National Institute for Science and Technology of Quantum Information (INCT-IQ/CNPq).

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, Roma, I-00185, Italy

    Nicolò Spagnolo, Chiara Vitelli, Marco Bentivegna, Fulvio Flamini, Sandro Giacomini, Giorgio Milani, Paolo Mataloni & Fabio Sciarrino

  2. Center of Life NanoScience @ La Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena, 255, Roma, I-00185, Italy

    Chiara Vitelli

  3. Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, RJ, 24210-340, Brazil

    Daniel J. Brod & Ernesto F. Galvão

  4. Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, Milano, I-20133, Italy

    Andrea Crespi, Roberta Ramponi & Roberto Osellame

  5. Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, Milano, I-20133, Italy

    Andrea Crespi, Roberta Ramponi & Roberto Osellame

Authors
  1. Nicolò Spagnolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chiara Vitelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marco Bentivegna
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Daniel J. Brod
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andrea Crespi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Fulvio Flamini
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sandro Giacomini
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Giorgio Milani
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Roberta Ramponi
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Paolo Mataloni
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Roberto Osellame
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Ernesto F. Galvão
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Fabio Sciarrino
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

N.S., C.V., M.B., D.J.B., P.M., R.O., E.F.G. and F.S. conceived the experimental approach for the validation of boson sampling. A.C., R.R. and R.O. fabricated and characterized the integrated devices using classical optics. N.S., C.V., M.B., F.F. and F.S. carried out the quantum experiments. S.G. and G.M. developed the data acquistion system. N.S., C.V., M.B., D.J.B., P.M., E.F.G. and F.S. elaborated the data. All authors discussed the experimental implementation and results, and contributed to writing the paper.

Corresponding authors

Correspondence to Roberto Osellame, Ernesto F. Galvão or Fabio Sciarrino.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 799 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Spagnolo, N., Vitelli, C., Bentivegna, M. et al. Experimental validation of photonic boson sampling. Nature Photon 8, 615–620 (2014). https://doi.org/10.1038/nphoton.2014.135

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2014.135

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing