Abstract

Quantum walks are powerful kernels in quantum computing protocols, and possess strong capabilities in speeding up various simulation and optimization tasks. One striking example is provided by quantum walkers evolving on glued trees1, which demonstrate faster hitting performances than classical random walks. However, their experimental implementation is challenging, as this involves highly complex arrangements of an exponentially increasing number of nodes. Here, we propose an alternative structure with a polynomially increasing number of nodes. We successfully map such graphs on quantum photonic chips using femtosecond-laser direct writing techniques in a geometrically scalable fashion. We experimentally demonstrate quantum fast hitting by implementing two-dimensional quantum walks on graphs with up to 160 nodes and a depth of eight layers, achieving a linear relationship between the optimal hitting time and the network depth. Our results open up a scalable path towards quantum speed-up in classically intractable complex problems.

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Acknowledgements

The authors thank J. D. Whitfield for a very useful conversation on numerical methods for the quantum stochastic walks, and J.-W. Pan for helpful discussions. This research is supported by the National Key R&D Program of China (2017YFA0303700), the National Natural Science Foundation of China (11690033, 61734005, 11761141014, 11374211), the Science and Technology Commission of Shanghai Municipality (STCSM) (15QA1402200, 16JC1400405, 17JC1400403), Shanghai Municipal Education Commission (SMEC) (16SG09, 2017-01-07-00-02-E00049) and the open fund from the State Key Laboratory of High Performance Computing (HPCL) (no. 201511-01). C.D.F. is funded by the Singapore National Research Foundation (Fellowship NRF-NRFF2016-02). M.S.K. is supported by the Samsung Global Research Outreach (GRO) project, the Korea Institute of Science and Technology (KIST) Institutional Program (2E26680-18-P025), the Engineering and Physical Sciences Research Council (EPSRC) (EP/K034480/1) and the Royal Society. X.-M.J. acknowledges support from the National Young 1000 Talents Plan.

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Affiliations

  1. State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China

    • Hao Tang
    • , Zi-Yu Shi
    • , Tian-Shen He
    • , Zhen Feng
    • , Jun Gao
    • , Ke Sun
    • , Zhan-Ming Li
    • , Zhi-Qiang Jiao
    • , Tian-Yu Wang
    •  & Xian-Min Jin
  2. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

    • Hao Tang
    •  & Xian-Min Jin
  3. Synergetic Innovation Centre of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China

    • Hao Tang
    • , Zi-Yu Shi
    • , Zhen Feng
    • , Jun Gao
    • , Zhan-Ming Li
    • , Zhi-Qiang Jiao
    •  & Xian-Min Jin
  4. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    • Carlo Di Franco
  5. Complexity Institute, Nanyang Technological University, Singapore, Singapore

    • Carlo Di Franco
  6. QOLS, Blackett Laboratory, Imperial College London, London, UK

    • M. S. Kim
  7. Korea Institute of Advanced Study, Dongdaemoon-Gu, Seoul, South Korea

    • M. S. Kim

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Contributions

X.-M.J. and M.S.K. conceived and supervised the project. H.T. and X.-M.J. designed the experiment. C.D.F., M.S.K. and T.-S.H. conducted the theoretical work. H.T., Z.-Y.S., J.G., K.S., Z.-Q.J. and X.-M.J. performed the single-photon experiment. H.T., Z.-M.L. and T.-Y.W. analysed the experimental data. Z.F. and Z.-Y.S. conducted chip fabrication. H.T., C.D.F., M.S.K. and X.-M.J. wrote the paper, with input from all the other authors.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Xian-Min Jin.

Supplementary information

  1. Supplementary Information

    Supplementary notes and figures.

  2. Supplementary Video 1

    Quantum fast hitting dynamics.

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DOI

https://doi.org/10.1038/s41566-018-0282-5