Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor
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Programmable silicon photonics realizes universal control over quantum walks.
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Recent works reported 2D continuous-time quantum walks of correlated photons, relying on arrays of coupled waveguides, and important results have also been achieved by means of superconductive quantum processors.
“Recent works reported 2D continuous-time quantum walks of correlated photons, relying on arrays of coupled waveguides 21,38,52 , and important results have been also achieved by means of superconductive quantum processors 6 .”
From Quantum walks of two correlated photons in a 2D synthetic lattice (2022) · cites this paper as [52]
The Introduction reports quantum walks in arrays of evanescently coupled waveguides, and the References list a study of correlated photon pairs in two-dimensional waveguide arrays. But this paper’s own Results describe a reconfigurable silicon photonic circuit, not a 2D coupled-waveguide array, so it supports the background claim rather than serving as an example of that implementation. The superconducting-processor clause is attached to a different citation. (LLM, conf=0.85)
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Cites
Quantum Walks of Correlated Photons
Peruzzo, A., Lobino, M., Matthews, J. C. F., Matsuda, N., Politi, A., Poulios, K., Zhou, X.-Q., Lahini, Y., Ismail, N., Wörhoff, K., et al. (2010) · Science · doi:10.1126/science.1193515 · Cited by 929 · cited 2× · see citing works
“Further application of quantum walks can be explored using multiple quantum walkers ( 14 ).”
BackgroundSelf-citationExponential algorithmic speedup by a quantum walk
Childs, A. M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., & Spielman, D. A. (2003) · Proceedings of the thirty-fifth annual ACM symposium on Theory of computing · doi:10.1145/780542.780552 · Cited by 825 · see citing works
Integrated multimode interferometers with arbitrary designs for photonic boson sampling
Crespi, A., Osellame, R., Ramponi, R., Brod, D. J., Galvão, E. F., Spagnolo, N., Vitelli, C., Maiorino, E., Mataloni, P., & Sciarrino, F. (2013) · Nature Photonics · doi:10.1038/nphoton.2013.112 · Cited by 662 · cited 2× · see citing works
“…over the recent years ( 24 , 26 , 30 , 31 ), including a silica nonreconfig-urable multipath unitary that is fixed at the point of fabrication ( 30 ), reconfigurability over six paths in silica ( 31 ), programmable optical circuits in silicon ( 24 ), and multiple reconfigurable two-mode…”
BackgroundMethodPhotons Walking the Line: A Quantum Walk with Adjustable Coin Operations
Schreiber, A., Cassemiro, K. N., Potoček, V., Gábris, A., Mosley, P. J., Andersson, E., Jex, I., & Silberhorn, C. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.050502 · Cited by 588 · see citing works
Two-Particle Bosonic-Fermionic Quantum Walk via Integrated Photonics
Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., & Osellame, R. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.010502 · Cited by 578 · see citing works
Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice
Rom, T., Best, T., van Oosten, D., Schneider, U., Fölling, S., Paredes, B., & Bloch, I. (2006) · Nature · doi:10.1038/nature05319 · Cited by 268 · see citing works
Statistically induced phase transitions and anyons in 1D optical lattices
Keilmann, T., Lanzmich, S., McCulloch, I., & Roncaglia, M. (2011) · Nature Communications · doi:10.1038/ncomms1353 · Cited by 199 · see citing works
Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays
Poulios, K., Keil, R., Fry, D., Meinecke, J. D. A., Matthews, J. C. F., Politi, A., Lobino, M., Gräfe, M., Heinrich, M., Nolte, S., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.143604 · Cited by 148 · cited 1× · see citing works
“2 of 9 larger graph (14, 36), we can program particle properties to access geometries of larger single-particle Hamiltonians that are otherwise beyond the capabilities of a fixed-size universal linear optics circuit acting on single photons or coherent light.”
BackgroundSelf-citationTwo-photon quantum walks in an elliptical direct-write waveguide array
Owens, J. O., Broome, M. A., Biggerstaff, D. N., Goggin, M. E., Fedrizzi, A., Linjordet, T., Ams, M., Marshall, G. D., Twamley, J., Withford, M. J., et al. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/7/075003 · Cited by 135 · see citing works
Experimental realization of a quantum quincunx by use of linear optical elements
Do, B., Stohler, M. L., Balasubramanian, S., Elliott, D. S., Eash, C., Fischbach, E., Fischbach, M. A., Mills, A., & Zwickl, B. (2005) · Journal of the Optical Society of America B · doi:10.1364/josab.22.000499 · Cited by 128 · see citing works
Observing fermionic statistics with photons in arbitrary processes
Matthews, J. C. F., Poulios, K., Meinecke, J. D. A., Politi, A., Peruzzo, A., Ismail, N., Wörhoff, K., Thompson, M. G., & O'Brien, J. L. (2013) · Scientific Reports · doi:10.1038/srep01539 · Cited by 98 · cited 6× · see citing works
“While in our scheme, for example, a sample from the output states of P-boson quantum walk can be obtained via P photons entering P copies of N-dimensional optical circuits (34), with polynomial complexity [i.”
BackgroundMethodInfluentialSelf-citation
Flagged first, then by citations
Research works printed but not linked: 39
- [3]A. M. Childs, D. Gosset, Z. Webb, Universal computation by multiparticle quantum walk. Science 339, 791– 794 (2013). 23413349
- [5]M. Mohseni, P. Rebentrost, S. Lloyd, A. Aspuru-Guzik, Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008). 19045332
- [7]A. M. Childs, J. Goldstone, Spatial search by quantum walk. Phys. Rev. A 70, 022314 (2004).
- [8]B. L. Douglas, J. B. Wang, A classical approach to the graph isomorphism problem using quantum walks. J. Phys. A 41, 075303 (2008).
- [9]J. K. Gamble, M. Friesen, D. Zhou, R. Joynt, S. N. Coppersmith, Two-particle quantum walks applied to the graph isomorphism problem. Phys. Rev. A 81, 052313 (2010).
- [11]E. Sánchez-Burillo, J. Duch, J. Gómez-Gardeñes, D. Zueco, Quantum navigation and ranking in complex networks. Sci. Rep. 2, 605 (2012). 22930671 PMC3428603
- [13]M. Pant, D. Towsley, D. Englund, S. Guha, Percolation thresholds for photonic quantum computing. Nat. Commun. 10, 1070 (2019). 30842425 PMC6403388
- [15]A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, I. A. Walmsley, Distinguishability and many-particle interference. Phys. Rev. Lett. 118, 153603 (2017). 28452506
- [16]A. A. Melnikov, L. E. Fedichkin, Quantum walks of interacting fermions on a cycle graph. Sci. Rep. 6, 34226 (2016). 27681057 PMC5041091
- [18]S. Aaronson, A. Arkhipov, The computational complexity of linear optics, in Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (ACM, New York, 2011), pp. 333–342.
- [19]J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, R. Han, Experimental implementation of the quantum random-walk algorithm. Phys. Rev. A 67, 042316 (2003).
- [20]H. Schmitz, R. Matjeschk, C. Schneider, J. Glueckert, M. Enderlein, T. Huber, T. Schaetz, Quantum walk of a trapped ion in phase space. Phys. Rev. Lett. 103, 090504 (2009). 19792773
- [21]M. Karski, L. Förster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede, A. Widera, Quantum walk in position space with single optically trapped atoms. Science 325, 174– 177 (2009). 19589996
- [25]X. Qiang, T. Loke, A. Montanaro, K. Aungskunsiri, X. Zhou, J. L. O’Brien, J. B. Wang, J. C. F. Matthews, Efficient quantum walk on a quantum processor. Nat. Commun. 7, 11511 (2016). 27146471 PMC4858748
- [28]H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, Y. Silberberg, Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008). 18518267
- [29]J. D. A. Meinecke, K. Poulios, A. Politi, J. C. F. Matthews, A. Peruzzo, N. Ismail, K. Wörhoff, J. L. O’Brien, M. G. Thompson, Coherent time evolution and boundary conditions of two-photon quantum walks in waveguide arrays. Phys. Rev. A 88, 012308 (2013).
- [31]J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, A. Laing, Universal linear optics. Science 349, 711– 716 (2015). 26160375
- [35]M. Reck, A. Zeilinger, H. Bernstein, P. Bertani, Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58– 61 (1994). 10056719
- [39]J. J. Renema, A. Menssen, W. R. Clements, G. Triginer, W. S. Kolthammer, I. A. Walmsley, Efficient classical algorithm for boson sampling with partially distinguishable photons. Phys. Rev. Lett. 120, 220502 (2018). 29906153
- [40]Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, Y.-H. Kim, Nonmonotonic quantum-to-classical transition in multiparticle interference. Proc. Natl. Acad. Sci. 110, 1227– 1231 (2013). 23297196 PMC3557023
- [41]M. Tillmann, S.-H. Tan, S. E. Stoeckl, B. C. Sanders, H. de Guise, R. Heilmann, S. Nolte, A. Szameit, P. Walther, Generalized multiphoton quantum interference. Phys. Rev. X 5, 041015 (2015).
- [43]S. Chakraborty, L. Novo, A. Ambainis, Y. Omar, Spatial search by quantum walk is optimal for almost all graphs. Phys. Rev. Lett. 116, 100501 (2016). 27015464
- [44]M. Cattaneo, M. A. C. Rossi, M. G. A. Paris, S. Maniscalco, Quantum spatial search on graphs subject to dynamical noise. Phys. Rev. A 98, 052347 (2018).
- [45]S. Chakraborty, L. Novo, S. D. Giorgio, Y. Omar, Optimal quantum spatial search on random temporal networks. Phys. Rev. Lett. 119, 220503 (2017). 29286791
- [46]L. Babai, Graph isomorphism in quasipolynomial time, in Proceedings of the 48th annual ACM Symposium on Theory of Computing (ACM, 2016), pp. 684–697.
- [47]I. Hen, A. P. Young, Solving the graph-isomorphism problem with a quantum annealer. Phys. Rev. A 86, 042310 (2012).
- [48]P. W. Mills, R. P. Rundle, J. H. Samson, S. J. Devitt, T. Tilma, V. M. Dwyer, M. J. Everitt, Quantum invariants and the graph isomorphism problem. Phys. Rev. A 100, 052317 (2019).
- [49]K. Brádler, S. Friedland, J. Izaac, N. Killoran, D. Su, Graph isomorphism and gaussian boson sampling. arXiv: 1810.10644 (2018). · arXiv
- [50]D. Emms, E. R. Hancock, S. Severini, R. C. Wilson, A matrix representation of graphs and its spectrum as a graph invariant. Electron. J. Comb. 13, R34 (2006).
- [51]S. D. Berry, J. B. Wang, Two-particle quantum walks: Entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011).
- [52]K. Rudinger, J. K. Gamble, M. Wellons, E. Bach, M. Friesen, R. Joynt, S. N. Coppersmith, Noninteracting multiparticle quantum random walks applied to the graph isomorphism problem for strongly regular graphs. Phys. Rev. A 86, 022334 (2012).
- [55]M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, T. F. Krauss, M. J. Steel, A. S. Clark, B. J. Eggleton, Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun. 4, 2582 (2013). 24107840 PMC3826656
- [57]C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, J. L. O’Brien, 60 db high-extinction auto-configured Mach–Zehnder interferometer. Opt. Lett. 41, 5318– 5321 (2016). 27842122
- [58]J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, D. Englund, High-fidelity quantum state evolution in imperfect photonic integrated circuits. Phys. Rev. A 92, 032322 (2015).
- [61]J. A. Izaac, J. B. Wang, Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions. Phys. Rev. E 96, 032136 (2017). 29346966
- [62]X. Qiang, X. Yang, J. Wu, X. Zhu, An enhanced classical approach to graph isomorphism using continuous-time quantum walk. J. Phys. A 45, 045305 (2012).
- [66]J. Smith, Algebraic aspects of multi-particle quantum walks, PhD thesis, University of Waterloo (2012).
- [67]H. Wang, J. Wu, X. Yang, X. Yi, A graph isomorphism algorithm using signatures computed via quantum walk search model. J. Phys. A 48, 115302 (2015).
- [68]Y. Liu, M. Xiong, C. Wu, D. Wang, Y. Liu, J. Ding, A. Huang, X. Fu, X. Qiang, P. Xu, M. Deng, X. Yang, J. Wu, Sample caching Markov chain Monte Carlo approach to boson sampling simulation. New J. Phys. 22, 033022 (2020).
Cited by
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Quantum walks of two correlated photons in a 2D synthetic lattice
Esposito, C., Barros, M. R., Durán Hernández, A., Carvacho, G., Di Colandrea, F., Barboza, R., Cardano, F., Spagnolo, N., Marrucci, L., & Sciarrino, F. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00544-0 · Cited by 36 · see citing works
Multi-particle quantum walks on 3D integrated photonic chip
Zhou, W.-H., Wang, X.-W., Ren, R.-J., Fu, Y.-X., Chang, Y.-J., Xu, X.-Y., Tang, H., & Jin, X.-M. (2024) · Light: Science & Applications · doi:10.1038/s41377-024-01627-7 · Cited by 16 · see citing works
- Authors
- Qiang, X., Wang, Y., Xue, S., Ge, R., Chen, L., Liu, Y., Huang, A., Fu, X., Xu, P., Yi, T., Xu, F., Deng, M., Wang, J. B., Meinecke, J. D. A., Matthews, J. C. F., Cai, X., Yang, X., & Wu, J.
- Affiliations
- National University of Defense Technology (CN)
- Sun Yat-sen University (CN)
- National Innovation Institute of Defense Technology, AMS, 100071 Beijing, China.
- Beijing Academy of Quantum Information Sciences (CN)
- The University of Western Australia (AU)
- Max Planck Institute of Quantum Optics (DE)
- University of Bristol (GB)
- Corresponding author
- Qiang, Xiaogang
- Cai, Xinlun
- Wu, Junjie
- ORCID
- Venue
- Science Advances
- Published
- 2021-02-26
- Volume
- 7
- Issue
- 9
- ISSN
- 2375-2548 (ISSN-L)
- PMC
- PMC7909884
- OpenAlex
- W3133207140
- Cited by
- 96
- References
- 11
- Citations by year
- 2026: 9 · 2025: 18 · 2024: 19 · 2023: 19 · 2022: 24 · 2021: 7
- FWCI
- 6.10
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Science Advances (publishedVersion, cc-by-nc)
- PubMed Central (publishedVersion, cc-by-nc)
- UWA Profiles and Research Repository (UWA) (publishedVersion, cc-by-nc)
- PubMed (publishedVersion)
- Funders
- National Natural Science Foundation of China (11804389, 61632021)
- BAQIS Research Program (Y18G16)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Photonic and Optical Devices
- Keywords
- quantum walks, silicon photonics, indistinguishability, graph isomorphism testing, programmable quantum processors, continuous-variable quantum optics
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