Implementing large instances of quantum algorithms1,2,3,4,5 requires the processing of many quantum information carriers in a hardware platform that supports the integration of different components6. Although established semiconductor fabrication processes can integrate many photonic components7, the generation and algorithmic processing of many photons has been a bottleneck in integrated photonics. Here, we report the on-chip generation and algorithmic processing of quantum states of light with up to eight photons. Switching between different optical pumping regimes, we implement the scattershot8,9, Gaussian10 and standard boson sampling3,11,12,13,14 protocols in the same silicon chip, which integrates linear and nonlinear photonic circuitry. We use these results to benchmark a quantum algorithm for calculating molecular vibronic spectra4. Our techniques can be readily scaled for the on-chip implementation of specialized quantum algorithms with tens of photons, pointing the way to efficiency advantages over conventional computers15.
Access optionsAccess options
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.7492991.
Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring. In 35th Annual Symposium on Foundations of Computer Science 124–134 (IEEE, 1994).
Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).
Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. In Proceedings of the 43rd Annual ACM Symposium on Theory of Computing 333–342 (ACM, 2011).
Huh, J., Guerreschi, G. G., Peropadre, B., McClean, J. R. & Aspuru-Guzik, A. Boson sampling for molecular vibronic spectra. Nat. Photon. 9, 615–620 (2015).
Sparrow, C. et al. Simulating the vibrational quantum dynamics of molecules using photonics. Nature 557, 660–667 (2018).
Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).
Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 260, 285–291 (2018).
Lund, A. P. et al. Boson sampling from a Gaussian state. Phys. Rev. Lett. 113, 100502 (2014).
Bentivegna, M. et al. Experimental scattershot boson sampling. Sci. Adv. 1, e1400255 (2015).
Hamilton, C. S. et al. Gaussian boson sampling. Phys. Rev. Lett. 119, 170501 (2017).
Broome, M. A. et al. Photonic boson sampling in a tunable circuit. Science 339, 794–798 (2013).
Spring, J. B. et al. Boson sampling on a photonic chip. Science 339, 798–801 (2013).
Crespi, A. et al. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nat. Photon. 7, 545–549 (2013).
Tillmann, M. et al. Experimental boson sampling. Nat. Photon. 7, 540–544 (2013).
Neville, A. et al. Classical boson sampling algorithms with superior performance to near-term experiments. Nat. Phys. 13, 1153–1157 (2017).
Olivares, D. G., Peropadre, B., Aspuru-Guzik, A. & García-Ripoll, J. J. Quantum simulation with a boson sampling circuit. Phys. Rev. A 94, 022319 (2016).
Arrazola, J. M. & Bromley, T. R. Using Gaussian boson sampling to find dense subgraphs. Phys. Rev. Lett. 121, 030503 (2018).
Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015).
Harris, N. C. et al. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photon. 11, 447–452 (2017).
Pernice, W. H. P. et al. High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits. Nat. Commun. 3, 1325 (2012).
Harris, N. C. et al. Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems. Phys. Rev. X 4, 041047 (2014).
Silverstone, J. W. et al. On-chip quantum interference between silicon photon-pair sources. Nat. Photon. 8, 104–108 (2014).
Spring, J. B. et al. Chip-based array of near-identical, pure, heralded single-photon sources. Optica 4, 90–96 (2017).
Ding, X. et al. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016).
Somaschi, N. et al. Near-optimal single-photon sources in the solid state. Nat. Photon. 10, 340–345 (2016).
Loredo, J. C. et al. Boson sampling with single-photon Fock states from a bright solid-state source. Phys. Rev. Lett. 118, 130503 (2017).
Wang, H. et al. High-efficiency multiphoton boson sampling. Nat. Photon. 11, 361–365 (2017).
Wang, H. et al. Toward scalable boson sampling with photon loss. Phys. Rev. Lett. 120, 230502 (2018).
Laucht, A. et al. A waveguide-coupled on-chip single-photon source. Phys. Rev. X 2, 011014 (2012).
Arcari, M. et al. Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide. Phys. Rev. Lett. 113, 093603 (2014).
Zhong, H.-S. et al. 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Phys. Rev. Lett. 121, 250505 (2018).
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, 5348–5350 (2014).
Ding, Y., Ou, H. & Peucheret, C. Ultra-high-efficiency apodized grating coupler using fully etched photonic crystals. Opt. Lett. 38, 2732–2734 (2013).
Christ, A., Laiho, K., Eckstein, A., Cassemiro, K. N. & Silberhorn, C. Probing multimode squeezing with correlation functions. New J. Phys. 13, 033027 (2011).
Bentivegna, M. et al. Bayesian approach to boson sampling validation. Int. J. Quantum Inf. 12, 1560028 (2014).
Spagnolo, N. et al. Experimental validation of photonic boson sampling. Nat. Photon. 8, 615–620 (2014).
Carolan, J. et al. On the experimental verification of quantum complexity in linear optics. Nat. Photon. 8, 621–626 (2014).
Caianiello, E. R. Combinatorics and Renormalization in Quantum Field Theory (W. A. Benjamin, 1973).
Kruse, R. et al. A detailed study of Gaussian boson sampling. Preprint at https://arxiv.org/abs/1801.07488 (2018).
Clements, W. R. et al. Approximating vibronic spectroscopy with imperfect quantum optics. J. Phys. B At. Mol. Opt. Phys. 51, 245503 (2018).
Shen, Y. et al. Quantum optical emulation of molecular vibronic spectroscopy using a trapped-ion device. Chem. Sci. 9, 836–840 (2018).
Wilkes, C. M. et al. 60 dB high-extinction auto-configured Mach–Zehnder interferometer. Opt. Lett. 41, 5318–5321 (2016).
Caspani, L. et al. Integrated sources of photon quantum states based on nonlinear optics. Light. Sci. Appl. 6, e17100 (2017).
Schuck, C. et al. Matrix of integrated superconducting single-photon detectors with high timing resolution. IEEE Trans. Appl. Supercond. 23, 2201007 (2013).
The authors thank N. Maraviglia, R. Chadwick, C. Sparrow, L. Banchi, G. Sinclair and D. Bacco for useful discussions and W.A. Murray, M. Loutit, E. Johnston, H. Fedder, M. Schlagmüller, M. Borghi and J. Lennon for technical assistance. The authors acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC), the European Research Council (ERC) and European Commission (EC) funded grants PICQUE, BBOI, QuChip, QuPIC, QITBOX, Quantera-eranet Square, VILLUM FONDEN, QUANPIC (ref. 00025298) and the Center of Excellence, Denmark SPOC (ref. DNRF123). J.W. acknowledges support from the Beijing Academy of Quantum Information Sciences (Y18G21) and from The Key R&D Program of Guangdong province (2018B030329001). A.L. acknowledges fellowship support from EPSRC (EP/N003470/1).
The authors declare no competing interests.
Peer review information: Nature Physics thanks Sonja Barkhofen, Robert Keil and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary notes and figures.