Photonics is a promising platform for implementing universal quantum information processing. Its main challenges include precise control of massive circuits of linear optical components and effective implementation of entangling operations on photons. By using large-scale silicon photonic circuits to implement an extension of the linear combination of quantum operators scheme, we realize a fully programmable two-qubit quantum processor, enabling universal two-qubit quantum information processing in optics. The quantum processor is fabricated with mature CMOS-compatible processing and comprises more than 200 photonic components. We programmed the device to implement 98 different two-qubit unitary operations (with an average quantum process fidelity of 93.2 ± 4.5%), a two-qubit quantum approximate optimization algorithm, and efficient simulation of Szegedy directed quantum walks. This fosters further use of the linear-combination architecture with silicon photonics for future photonic quantum processors.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

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

  2. 2.

    Silverstone, J. W., Bonneau, D., O’Brien, J. L. & Thompson, M. G. Silicon quantum photonics. IEEE J. Sel. Top. Quantum Electron. 22, 390–402 (2016).

  3. 3.

    O’Brien, J. L., Furusawa, A. & Vučković, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009).

  4. 4.

    Wilkes, C. M. et al. 60 dB high-extinction auto-configured Mach–Zehnder interferometer. Opt. Lett. 41, 5318–5321 (2016).

  5. 5.

    Sun, J., Timurdogan, E., Yaacobi, A., Hosseini, E. S. & Watts, M. R. Large-scale nanophotonic phased array. Nature 493, 195–199 (2013).

  6. 6.

    Harris, N. C. et al. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photon. 11, 447–452 (2017).

  7. 7.

    Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

  8. 8.

    Zhou, X. Q. et al. Adding control to arbitrary unknown quantum operations. Nat. Commun. 2, 413 (2011).

  9. 9.

    Long, G. L. General quantum interference principle and duality computer. Commun. Theor. Phys. 45, 825–844 (2006).

  10. 10.

    Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O’Brien, J. L. Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008).

  11. 11.

    Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 1500–1503 (2010).

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

    Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285–291 (2018).

  16. 16.

    Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015).

  17. 17.

    Sharping, J. E. et al. Generation of correlated photons in nanoscale silicon waveguides. Opt. Express 14, 12388–12393 (2006).

  18. 18.

    Najafi, F. et al. On-chip detection of entangled photons by scalable integration of single-photon detectors. Nat. Commun. 6, 5873 (2014).

  19. 19.

    Debnath, S. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016).

  20. 20.

    Vandersypen, L. M. K. et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001).

  21. 21.

    Song, C. et al. 10-qubit entanglement and parallel logic operations with a superconducting circuit. Phys. Rev. Lett. 119, 180511 (2017).

  22. 22.

    Martn-López, E. et al. Experimental realization of Shor’s quantum factoring algorithm using qubit recycling. Nat. Photon. 6, 773–776 (2012).

  23. 23.

    Barz, S. et al. A two-qubit photonic quantum processor and its application to solving systems of linear equations. Sci. Rep. 4, 6115 (2014).

  24. 24.

    Wang, J. et al. Experimental quantum Hamiltonian learning. Nat. Phys. 13, 551–555 (2017).

  25. 25.

    Santagati, R. et al. Silicon photonic processor of two-qubit entangling quantum logic. J. Opt. 19, 114006 (2017).

  26. 26.

    Hanneke, D. et al. Realization of a programmable two-qubit quantum processor. Nat. Phys. 6, 13–16 (2010).

  27. 27.

    Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm. Preprint at https://arxiv.org/abs/1411.4028 (2014).

  28. 28.

    Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm applied to a bounded occurrence constraint problem. Preprint at https://arxiv.org/abs/1412.6062 (2014).

  29. 29.

    Szegedy, M. Spectra of quantized walks and a \(\sqrt {{\rm{\delta}}{\rm{\varepsilon}}}\) rule. Preprint at https://arxiv.org/abs/quant-ph/0401053 (2004).

  30. 30.

    Szegedy, M. in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science 32–41 (IEEE, 2004).

  31. 31.

    Childs, A. M. & Wiebe, N. Hamiltonian simulation using linear combinations of unitary operations. Quantum Inform. Comput. 12, 901–924 (2012).

  32. 32.

    Childs, A. M., Kothari, R. & Somma, R. D. Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM J. Comput. 46, 1920–1950 (2017).

  33. 33.

    Patel, R. B., Ho, J., Ferreyrol, F., Ralph, T. C. & Pryde, G. J. A quantum Fredkin gate. Sci. Adv. 2, e1501531 (2016).

  34. 34.

    Wei, S. J., Ruan, D. & Long, G. L. Duality quantum algorithm efficiently simulates open quantum systems. Sci. Rep. 6, 30727 (2016).

  35. 35.

    Qiang, X., Zhou, X., Aungskunsiri, K., Cable, H. & O’Brien, J. L. Quantum processing by remote quantum control. Quantum Sci. Technol. 2, 045002 (2017).

  36. 36.

    Silverstone, J. W. et al. On-chip quantum interference between silicon photon-pair sources. Nat. Photon. 8, 104–108 (2014).

  37. 37.

    Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).

  38. 38.

    Okamoto, R. et al. An entanglement filter. Science 323, 483–485 (2009).

  39. 39.

    Farhi, E. & Harrow, A. W. Quantum supremacy through the quantum approximate optimization algorithm. Preprint at https://arxiv.org/abs/1602.07674 (2016).

  40. 40.

    Childs, A. M., Gosset, D. & Webb, Z. Universal computation by multiparticle quantum walk. Science 339, 791–794 (2013).

  41. 41.

    Childs, A. M. & Goldstone, J. Spatial search by quantum walk. Phys. Rev. A 70, 022314 (2004).

  42. 42.

    Paparo, G. D. & Martin-Delgado, M. A. Google in a quantum network. Sci. Rep. 2, 444 (2012).

  43. 43.

    Paparo, G. D., Müller, M., Comellas, F. & Martin-Delgado, M. A. Quantum Google in a complex network. Sci. Rep. 3, 2773 (2013).

  44. 44.

    Loke, T., Tang, J. W., Rodriguez, J., Small, M. & Wang, J. B. Comparing classical and quantum pageranks. Quantum Inf. Process. 16, 25 (2017).

  45. 45.

    Chiang, C.-F., Nagaj, D. & Wocjan, P. Efficient circuits for quantum walks. Quantum Inform. Comput. 10, 420–434 (2010).

  46. 46.

    Loke, T. & Wang, J. B. Efficient quantum circuits for Szegedy quantum walks. Ann. Phys. 382, 64–84 (2017).

  47. 47.

    Highchi, Y., Konno, N., Sato, I. & Segawa, E. Periodicity of the discrete-time quantum walk on a finite graph. Interdiscip. Inform. Sci. 23, 75–86 (2017).

  48. 48.

    Collins, M. J. et al. Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun. 4, 2582 (2013).

  49. 49.

    Khasminskaya, S. et al. Fully integrated quantum photonic circuit with an electrically driven light source. Nat. Photon. 10, 727–732 (2016).

  50. 50.

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

  51. 51.

    Qiang, X. et al. Underpinning data for ‘Large-scale silicon quantum photonics implementing arbitrary two-qubit processing.’ https://doi.org/10.5523/bris.1gbf7bpuazruz26cxh0tc0q9zq (2018).

Download references


The authors thank S. Paesani, J. Silverstone, G. Sinclair, K. Aungskunsiri and C. Sparrow for helpful discussions and A. Murray and M. Loutit for assistance with wire-bonding the device. This work was supported by EPSRC programme grant EP/L024020/1, US Army Research Office (ARO) grant no. W911NF-14-1-0133, US Air Force Office of Scientific Research (AFOSR) and the Centre for Nanoscience and Quantum Information (NSQI). X.Q. acknowledges support from the China Scholarship Council and the National Natural Science Foundation of China (NSFC no. 61632021). X.Z. acknowledges support from the National Key Research and Development Program (2017YFA0305200 and 2016YFA0301700), the National Young 1000 Talents Plan, and the Natural Science Foundation of Guangdong (2016A030312012). J.W. acknowledges support from the National Young 1000 Talents Plan. T.C.R. acknowledges support from the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project no. CE170100012). J.L.O.B. acknowledges a Royal Society Wolfson Merit Award and a Royal Academy of Engineering Chair in Emerging Technologies. M.G.T. acknowledges support from the ERC starter grant ERC-2014-STG 640079 and an EPSRC Early Career Fellowship EP/K033085/1. J.C.F.M acknowledges support from EPSRC Early Career Fellowship EP/M024385/1.

Author information


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

    • Xiaogang Qiang
    • , Jianwei Wang
    • , Callum M. Wilkes
    • , Sean O’Gara
    • , Laurent Kling
    • , Graham D. Marshall
    • , Raffaele Santagati
    • , Jeremy L. O’Brien
    • , Mark G. Thompson
    •  & Jonathan C. F. Matthews
  2. Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha, China

    • Xiaogang Qiang
  3. National Innovation Institute of Defense Technology, AMS, Beijing, China

    • Xiaogang Qiang
  4. State Key Laboratory of Optoelectronic Materials and Technologies and School of Physics, Sun Yat-sen University, Guangzhou, China

    • Xiaoqi Zhou
  5. State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Centre of Quantum Matter, School of Physics, Peking University, Beijing, China

    • Jianwei Wang
  6. School of Physics, The University of Western Australia, Crawley, Western Australia, Australia

    • Thomas Loke
    •  & Jingbo B. Wang
  7. Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland, Australia

    • Timothy C. Ralph


  1. Search for Xiaogang Qiang in:

  2. Search for Xiaoqi Zhou in:

  3. Search for Jianwei Wang in:

  4. Search for Callum M. Wilkes in:

  5. Search for Thomas Loke in:

  6. Search for Sean O’Gara in:

  7. Search for Laurent Kling in:

  8. Search for Graham D. Marshall in:

  9. Search for Raffaele Santagati in:

  10. Search for Timothy C. Ralph in:

  11. Search for Jingbo B. Wang in:

  12. Search for Jeremy L. O’Brien in:

  13. Search for Mark G. Thompson in:

  14. Search for Jonathan C. F. Matthews in:


X.Z., X.Q., T.C.R., J.L.O.B. and J.C.F.M. conceived and designed the project. X.Z. and X.Q. designed the device. X.Q., J.W., C.M.W., L.K., G.D.M. and R.S. built the experimental set-up and carried out the experiments. X.Q., X.Z., T.L., S.O.G., J.B.W. and J.C.F.M. performed the theoretical analysis. X.Z., J.L.O.B., M.G.T. and J.C.F.M. managed the project. All authors discussed the results and contributed to writing the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Xiaoqi Zhou or Jonathan C. F. Matthews.

Supplementary information

  1. Supplementary Information

    Supplementary notes and figures.

About this article

Publication history