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Experimental quantum fast hitting on hexagonal graphs

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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Fig. 1: Theoretical graphs and their implementation on photonic chips.
Fig. 2: Fast hitting on a two-layered hexagonal graph.
Fig. 3: Increasing the complexity of hexagonal graphs.
Fig. 4: Comparison between quantum hitting and classical hitting.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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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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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.

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Correspondence to Xian-Min Jin.

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Supplementary Video 1

Quantum fast hitting dynamics.

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Tang, H., Di Franco, C., Shi, ZY. et al. Experimental quantum fast hitting on hexagonal graphs. Nature Photon 12, 754–758 (2018). https://doi.org/10.1038/s41566-018-0282-5

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