{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,31]],"date-time":"2025-08-31T23:33:35Z","timestamp":1756683215963,"version":"3.37.3"},"reference-count":74,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T00:00:00Z","timestamp":1555718400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s11128-019-2286-6","type":"journal-article","created":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T14:02:37Z","timestamp":1555768957000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Quantum path computing: computing architecture with propagation paths in multiple plane diffraction of classical sources of fermion and boson particles"],"prefix":"10.1007","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3756-3280","authenticated-orcid":false,"given":"Burhan","family":"Gulbahar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,4,20]]},"reference":[{"key":"2286_CR1","volume-title":"Quantum Mechanics and Path Integrals","author":"RP Feynman","year":"2010","unstructured":"Feynman, R.P., Hibbs, A.R., Styer, D.F.: Quantum Mechanics and Path Integrals, emended edn. Dover Publications, New York (2010)","edition":"emended"},{"key":"2286_CR2","doi-asserted-by":"publisher","first-page":"042319","DOI":"10.1103\/PhysRevA.69.042319","volume":"69","author":"G Puentes","year":"2004","unstructured":"Puentes, G., La Mela, C., Ledesma, S., Iemmi, C., Paz, J.P., Saraceno, M.: Optical simulation of quantum algorithms using programmable liquid-crystal displays. Phys. Rev. A 69, 042319 (2004)","journal-title":"Phys. Rev. A"},{"key":"2286_CR3","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1007\/s10701-010-9452-0","volume":"40","author":"V Vedral","year":"2010","unstructured":"Vedral, V.: The elusive source of quantum speedup. Found. Phys. 40, 1141 (2010)","journal-title":"Found. Phys."},{"key":"2286_CR4","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1103\/PhysRevA.48.116","volume":"48","author":"V \u010cern\u00fd","year":"1993","unstructured":"\u010cern\u00fd, V.: Quantum computers and intractable (NP-complete) computing problems. Phys. Rev. A 48, 116 (1993)","journal-title":"Phys. Rev. A"},{"key":"2286_CR5","doi-asserted-by":"publisher","first-page":"10473","DOI":"10.1364\/OE.15.010473","volume":"15","author":"T Haist","year":"2007","unstructured":"Haist, T., Osten, W.: An optical solution for the traveling salesman problem. Opt. Express 15, 10473 (2007)","journal-title":"Opt. Express"},{"key":"2286_CR6","doi-asserted-by":"publisher","first-page":"021002","DOI":"10.1088\/0953-4075\/42\/2\/021002","volume":"42","author":"AA Rangelov","year":"2009","unstructured":"Rangelov, A.A.: Factorizing numbers with classical interference: several implementations in optics. J. Phys. B At. Mol. Opt. Phys. 42, 021002 (2009)","journal-title":"J. Phys. B At. Mol. Opt. Phys."},{"key":"2286_CR7","doi-asserted-by":"crossref","unstructured":"Aaronson, S., Arkhipov, A.: The computational complexity of linear optics. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, p. 333 (2011)","DOI":"10.1145\/1993636.1993682"},{"issue":"1","key":"2286_CR8","doi-asserted-by":"publisher","first-page":"016001","DOI":"10.1088\/1361-6633\/aad5b2","volume":"82","author":"F Flamini","year":"2018","unstructured":"Flamini, F., Spagnolo, N., Sciarrino, F.: Photonic quantum information processing: a review. Rep. Prog. Phys. 82(1), 016001 (2018)","journal-title":"Rep. Prog. Phys."},{"issue":"23","key":"2286_CR9","doi-asserted-by":"publisher","first-page":"230502","DOI":"10.1103\/PhysRevLett.120.230502","volume":"120","author":"H Wang","year":"2018","unstructured":"Wang, H., Li, W., Jiang, X., He, Y.M., Li, Y.H., Ding, X., Chen, M.C., Qin, J., Peng, C.Z., Schneider, C., Kamp, M.: Toward scalable boson sampling with photon loss. Phys. Rev. Lett. 120(23), 230502 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"2286_CR10","unstructured":"Gulbahar, B.: Quantum entanglement and interference in time with multi-plane diffraction and violation of Leggett\u2013Garg inequality without signaling. arXiv:1808.06477 (2018)"},{"issue":"6","key":"2286_CR11","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/BF01886518","volume":"16","author":"RP Feynman","year":"1986","unstructured":"Feynman, R.P.: Quantum mechanical computers. Found. Phys. 16(6), 507 (1986)","journal-title":"Found. Phys."},{"key":"2286_CR12","unstructured":"Bausch, J., Crosson, E.: Analysis and limitations of modified circuit-to-Hamiltonian constructions. arXiv:1609.08571 (2016)"},{"issue":"11","key":"2286_CR13","doi-asserted-by":"publisher","first-page":"113066","DOI":"10.1088\/1367-2630\/16\/11\/113066","volume":"16","author":"DG Tempel","year":"2014","unstructured":"Tempel, D.G., Aspuru-Guzik, A.: The Kitaev\u2013Feynman clock for open quantum systems. New J. Phys. 16(11), 113066 (2014)","journal-title":"New J. Phys."},{"key":"2286_CR14","volume-title":"Classical and Quantum Computation","author":"AY Kitaev","year":"2002","unstructured":"Kitaev, A.Y., Shen, A., Vyalyi, M.N., Vyalyi, M.N.: Classical and Quantum Computation, vol. 47. American Mathematical Society, Providence (2002)"},{"issue":"4","key":"2286_CR15","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1137\/080734479","volume":"50","author":"D Aharonov","year":"2008","unstructured":"Aharonov, D., Van Dam, W., Kempe, J., Landau, Z., Lloyd, S., Regev, O.: Adiabatic quantum computation is equivalent to standard quantum computation. SIAM Rev. 50(4), 755 (2008)","journal-title":"SIAM Rev."},{"key":"2286_CR16","doi-asserted-by":"publisher","first-page":"033621","DOI":"10.1103\/PhysRevA.93.033621","volume":"9","author":"IG daPaz","year":"2016","unstructured":"daPaz, I.G., Vieira, C.H.S., Ducharme, R., Cabral, L.A., Alexander, H., Sampaio, M.D.R.: Gouy phase in nonclassical paths in a triple-slit interference experiment. Phys. Rev. A 9, 033621 (2016)","journal-title":"Phys. Rev. A"},{"key":"2286_CR17","doi-asserted-by":"publisher","first-page":"120406","DOI":"10.1103\/PhysRevLett.113.120406","volume":"113","author":"R Sawant","year":"2014","unstructured":"Sawant, R., Samuel, J., Sinha, A., Sinha, S., Sinha, U.: Nonclassical paths in quantum interference experiments. Phys. Rev. Lett. 113, 120406 (2014)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"2286_CR18","doi-asserted-by":"publisher","first-page":"062306","DOI":"10.1103\/PhysRevA.97.062306","volume":"97","author":"L Caha","year":"2018","unstructured":"Caha, L., Landau, Z., Nagaj, D.: Clocks in Feynman\u2019s computer and Kitaev\u2019s local Hamiltonian: bias, gaps, idling, and pulse tuning. Phys. Rev. A 97(6), 062306 (2018)","journal-title":"Phys. Rev. A"},{"key":"2286_CR19","volume-title":"Consistent Quantum Theory","author":"RB Griffiths","year":"2003","unstructured":"Griffiths, R.B.: Consistent Quantum Theory. Cambridge University Press, Cambridge (2003)"},{"issue":"1\u20132","key":"2286_CR20","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF01015734","volume":"36","author":"RB Griffiths","year":"1984","unstructured":"Griffiths, R.B.: Consistent histories and the interpretation of quantum mechanics. J. Stat. Phys. 36(1\u20132), 219 (1984)","journal-title":"J. Stat. Phys."},{"issue":"15","key":"2286_CR21","doi-asserted-by":"publisher","first-page":"2201","DOI":"10.1103\/PhysRevLett.70.2201","volume":"70","author":"RB Griffiths","year":"1993","unstructured":"Griffiths, R.B.: Consistent interpretation of quantum mechanics using quantum trajectories. Phys. Rev. Lett. 70(15), 2201 (1993)","journal-title":"Phys. Rev. Lett."},{"key":"2286_CR22","unstructured":"Cotler, J., Wilczek, F.: Bell tests for histories. arXiv:1503.06458 (2015)"},{"key":"2286_CR23","doi-asserted-by":"publisher","first-page":"014004","DOI":"10.1088\/0031-8949\/2016\/T168\/014004","volume":"T168","author":"J Cotler","year":"2016","unstructured":"Cotler, J., Wilczek, F.: Entangled histories. Phys. Scr. T168, 014004 (2016)","journal-title":"Phys. Scr."},{"key":"2286_CR24","doi-asserted-by":"publisher","first-page":"032331","DOI":"10.1103\/PhysRevA.96.032331","volume":"96","author":"L Kocia","year":"2017","unstructured":"Kocia, L., Huang, Y., Love, P.: Semiclassical formulation of the Gottesman\u2013Knill theorem and universal quantum computation. Phys. Rev. A 96, 032331 (2017)","journal-title":"Phys. Rev. A"},{"key":"2286_CR25","volume-title":"Introduction to Quantum Mechanics: A Time-dependent Perspective","author":"DJ Tannor","year":"2007","unstructured":"Tannor, D.J.: Introduction to Quantum Mechanics: A Time-dependent Perspective. University Science Books, Sausalito (2007)"},{"key":"2286_CR26","doi-asserted-by":"crossref","unstructured":"Koh, D.E., Penney, M.D., Spekkens, R.W.: Computing quopit Clifford circuit amplitudes by the sum-over-paths technique. arXiv:1702.03316 (2017)","DOI":"10.26421\/QIC17.13-14-1"},{"issue":"1","key":"2286_CR27","doi-asserted-by":"publisher","first-page":"012331","DOI":"10.1103\/PhysRevA.97.012331","volume":"97","author":"X Yuan","year":"2018","unstructured":"Yuan, X., Zhou, H., Gu, M., Ma, X.: Unification of nonclassicality measures in interferometry. Phys. Rev. A 97(1), 012331 (2018)","journal-title":"Phys. Rev. A"},{"issue":"6816","key":"2286_CR28","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1038\/35051009","volume":"409","author":"E Knill","year":"2001","unstructured":"Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409(6816), 46 (2001)","journal-title":"Nature"},{"issue":"15\u201317","key":"2286_CR29","doi-asserted-by":"publisher","first-page":"2331","DOI":"10.1080\/09500340308233564","volume":"50","author":"SD Bartlett","year":"2003","unstructured":"Bartlett, S.D., Sanders, B.C.: Requirement for quantum computation. J. Mod. Opt. 50(15\u201317), 2331 (2003)","journal-title":"J. Mod. Opt."},{"issue":"4","key":"2286_CR30","doi-asserted-by":"publisher","first-page":"043807","DOI":"10.1103\/PhysRevA.73.043807","volume":"73","author":"M Sasaki","year":"2006","unstructured":"Sasaki, M., Suzuki, S.: Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: analytical formula. Phys. Rev. A 73(4), 043807 (2006)","journal-title":"Phys. Rev. A"},{"issue":"20","key":"2286_CR31","doi-asserted-by":"publisher","first-page":"207903","DOI":"10.1103\/PhysRevLett.89.207903","volume":"89","author":"SD Bartlett","year":"2002","unstructured":"Bartlett, S.D., Sanders, B.C.: Efficient classical simulation of optical quantum information circuits. Phys. Rev. Lett. 89(20), 207903 (2002)","journal-title":"Phys. Rev. Lett."},{"issue":"10","key":"2286_CR32","doi-asserted-by":"publisher","first-page":"100502","DOI":"10.1103\/PhysRevLett.113.100502","volume":"113","author":"AP Lund","year":"2014","unstructured":"Lund, A.P., Laing, A., Rahimi-Keshari, S., Rudolph, T., OBrien, J.L., Ralph, T.C.: Boson sampling from a Gaussian state. Phys. Rev. Lett. 113(10), 100502 (2014)","journal-title":"Phys. Rev. Lett."},{"issue":"17","key":"2286_CR33","doi-asserted-by":"publisher","first-page":"170501","DOI":"10.1103\/PhysRevLett.119.170501","volume":"119","author":"CS Hamilton","year":"2017","unstructured":"Hamilton, C.S., Kruse, R., Sansoni, L., Barkhofen, S., Silberhorn, C., Jex, I.: Gaussian boson sampling. Phys. Rev. Lett. 119(17), 170501 (2017)","journal-title":"Phys. Rev. Lett."},{"key":"2286_CR34","unstructured":"Rhode, P.P., Motes, K.R., Dowling, J.P.: Sampling generalized cat states with linear optics is probably hard. arXiv:1310.0297 (2013)"},{"key":"2286_CR35","doi-asserted-by":"crossref","unstructured":"Kruse, R., Hamilton, C.S., Sansoni, L., Barkhofen, S., Silberhorn, C., Jex, I.: A detailed study of Gaussian boson sampling. arXiv:1801.07488 (2018)","DOI":"10.1364\/CLEO_QELS.2017.FTu1F.2"},{"issue":"1","key":"2286_CR36","doi-asserted-by":"publisher","first-page":"16955","DOI":"10.1038\/s41598-018-35330-6","volume":"8","author":"II Arkhipov","year":"2018","unstructured":"Arkhipov, I.I., Barasi\u0144ski, A., Svozil\u00edk, J.: Negativity volume of the generalized Wigner function as an entanglement witness for hybrid bipartite states. Sci. Rep. 8(1), 16955 (2018)","journal-title":"Sci. Rep."},{"issue":"10","key":"2286_CR37","doi-asserted-by":"publisher","first-page":"4237","DOI":"10.1007\/s11128-016-1380-2","volume":"15","author":"F Siyouri","year":"2016","unstructured":"Siyouri, F., El Baz, M., Hassouni, Y.: The negativity of Wigner function as a measure of quantum correlations. Quantum Inf. Process. 15(10), 4237 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"2286_CR38","doi-asserted-by":"publisher","first-page":"042323","DOI":"10.1103\/PhysRevA.74.042323","volume":"74","author":"JP Dahl","year":"2006","unstructured":"Dahl, J.P., Mack, H., Wolf, A., Schleich, W.P.: Entanglement versus negative domains of Wigner functions. Phys. Rev. A 74(4), 042323 (2006)","journal-title":"Phys. Rev. A"},{"issue":"11","key":"2286_CR39","doi-asserted-by":"publisher","first-page":"113011","DOI":"10.1088\/1367-2630\/14\/11\/113011","volume":"14","author":"V Veitch","year":"2012","unstructured":"Veitch, V., Ferrie, C., Gross, D., Emerson, J.: Negative quasi-probability as a resource for quantum computation. New J. Phys. 14(11), 113011 (2012)","journal-title":"New J. Phys."},{"key":"2286_CR40","doi-asserted-by":"crossref","unstructured":"Albarelli, F., Genoni, M.G., Paris, M.G., Ferraro, A.: Resource theory of quantum non-Gaussianity and Wigner negativity. arXiv:1804.05763 (2018)","DOI":"10.1103\/PhysRevA.98.052350"},{"issue":"5","key":"2286_CR41","doi-asserted-by":"publisher","first-page":"052334","DOI":"10.1103\/PhysRevA.95.052334","volume":"95","author":"R Raussendorf","year":"2017","unstructured":"Raussendorf, R., Browne, D.E., Delfosse, N., Okay, C., Bermejo-Vega, J.: Contextuality and Wigner-function negativity in qubit quantum computation. Phys. Rev. A 95(5), 052334 (2017)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"2286_CR42","doi-asserted-by":"publisher","first-page":"013037","DOI":"10.1088\/1367-2630\/15\/1\/013037","volume":"15","author":"V Veitch","year":"2013","unstructured":"Veitch, V., Wiebe, N., Ferrie, C., Emerson, J.: Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation. New J. Phys. 15(1), 013037 (2013)","journal-title":"New J. Phys."},{"issue":"10","key":"2286_CR43","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1088\/1464-4266\/6\/10\/003","volume":"6","author":"A Kenfack","year":"2004","unstructured":"Kenfack, A., \u017byczkowski, K.: Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B Quantum Semiclass. Opt. 6(10), 396 (2004)","journal-title":"J. Opt. B Quantum Semiclass. Opt."},{"issue":"6","key":"2286_CR44","doi-asserted-by":"publisher","first-page":"066219","DOI":"10.1103\/PhysRevE.78.066219","volume":"78","author":"A Kowalewska-Kud\u0142aszyk","year":"2008","unstructured":"Kowalewska-Kud\u0142aszyk, A., Kalaga, J.K., Leo\u0144ski, W.: Wigner-function nonclassicality as indicator of quantum chaos. Phys. Rev. E 78(6), 066219 (2008)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"2286_CR45","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s10773-018-3913-1","volume":"58","author":"FZ Siyouri","year":"2019","unstructured":"Siyouri, F.Z.: Markovian and non-Markovian dynamics of non-classical correlations and Wigner function for GHZ-type coherent states. Int. J. Theor. Phys. 58(1), 103 (2019)","journal-title":"Int. J. Theor. Phys."},{"issue":"26","key":"2286_CR46","doi-asserted-by":"publisher","first-page":"263603","DOI":"10.1103\/PhysRevLett.121.263603","volume":"121","author":"F Quijandr\u00eda","year":"2018","unstructured":"Quijandr\u00eda, F., Strandberg, I., Johansson, G.: Steady-state generation of Wigner-negative states in one-dimensional resonance fluorescence. Phys. Rev. Lett. 121(26), 263603 (2018)","journal-title":"Phys. Rev. Lett."},{"issue":"11","key":"2286_CR47","doi-asserted-by":"publisher","first-page":"113016","DOI":"10.1088\/1367-2630\/aaea15","volume":"20","author":"JS Bennett","year":"2018","unstructured":"Bennett, J.S., Bowen, W.P.: Rapid mechanical squeezing with pulsed optomechanics. New J. Phys. 20(11), 113016 (2018)","journal-title":"New J. Phys."},{"issue":"18","key":"2286_CR48","doi-asserted-by":"publisher","first-page":"180501","DOI":"10.1103\/PhysRevLett.102.180501","volume":"102","author":"AM Childs","year":"2009","unstructured":"Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102(18), 180501 (2009)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"2286_CR49","doi-asserted-by":"publisher","first-page":"010502","DOI":"10.1103\/PhysRevLett.108.010502","volume":"108","author":"L Sansoni","year":"2012","unstructured":"Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., Osellame, R.: Two-particle bosonic\u2013fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108(1), 010502 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"2286_CR50","unstructured":"Singh, S., Chandrashekar, C.M.: Interference and correlated coherence in disordered and localized quantum walk. arXiv:1711.06217v2 (2018)"},{"key":"2286_CR51","doi-asserted-by":"publisher","first-page":"012310","DOI":"10.1103\/PhysRevA.69.012310","volume":"69","author":"H Jeong","year":"2004","unstructured":"Jeong, H., Paternostro, M., Kim, M.S.: Simulation of quantum random walks using the interference of a classical field. Phys. Rev. A 69, 012310 (2004)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"2286_CR52","doi-asserted-by":"publisher","first-page":"040302","DOI":"10.1103\/PhysRevA.92.040302","volume":"92","author":"SK Goyal","year":"2015","unstructured":"Goyal, S.K., Roux, F.S., Forbes, A., Konrad, T.: Implementation of multidimensional quantum walks using linear optics and classical light. Phys. Rev. A 92(4), 040302 (2015)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"2286_CR53","doi-asserted-by":"publisher","first-page":"eaat3174","DOI":"10.1126\/sciadv.aat3174","volume":"4","author":"H Tang","year":"2018","unstructured":"Tang, H., Lin, X.F., Feng, Z., Chen, J.Y., Gao, J., Sun, K., Wang, C.Y., Lai, P.C., Xu, X.Y., Wang, Y., Qiao, L.F.: Experimental two-dimensional quantum walk on a photonic chip. Sci. Adv. 4(5), eaat3174 (2018)","journal-title":"Sci. Adv."},{"key":"2286_CR54","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1126\/science.1218448","volume":"1218448","author":"A Schreiber","year":"2012","unstructured":"Schreiber, A., G\u00e1bris, A., Rohde, P.P., Laiho, K., \u0160tefa\u0148\u00e1k, M., Poto\u010dek, V., Hamilton, C., Jex, I., Silberhorn, C.: A 2D quantum walk simulation of two-particle dynamics. Science 1218448, 55\u201358 (2012)","journal-title":"Science"},{"issue":"2","key":"2286_CR55","doi-asserted-by":"publisher","first-page":"020301","DOI":"10.1103\/PhysRevA.68.020301","volume":"68","author":"PL Knight","year":"2003","unstructured":"Knight, P.L., Rold\u00e1n, E., Sipe, J.E.: Quantum walk on the line as an interference phenomenon. Phys. Rev. A 68(2), 020301 (2003)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"2286_CR56","doi-asserted-by":"publisher","first-page":"012310","DOI":"10.1103\/PhysRevA.69.012310","volume":"69","author":"H Jeong","year":"2004","unstructured":"Jeong, H., Paternostro, M., Kim, M.S.: Simulation of quantum random walks using the interference of a classical field. Phys. Rev. A 69(1), 012310 (2004)","journal-title":"Phys. Rev. A"},{"key":"2286_CR57","doi-asserted-by":"publisher","first-page":"28610","DOI":"10.1038\/srep28610","volume":"6","author":"F Qi","year":"2016","unstructured":"Qi, F., et al.: Experimentally simulating quantum walks with self-collimated light. Sci. Rep. 6, 28610 (2016)","journal-title":"Sci. Rep."},{"issue":"17","key":"2286_CR58","doi-asserted-by":"publisher","first-page":"170506","DOI":"10.1103\/PhysRevLett.100.170506","volume":"100","author":"HB Perets","year":"2008","unstructured":"Perets, H.B., Lahini, Y., Pozzi, F., Sorel, M., Morandotti, R., Silberberg, Y.: Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100(17), 170506 (2008)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"2286_CR59","doi-asserted-by":"publisher","first-page":"042330","DOI":"10.1103\/PhysRevA.81.042330","volume":"81","author":"NB Lovett","year":"2010","unstructured":"Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81(4), 042330 (2010)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"2286_CR60","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1007\/s11128-012-0432-5","volume":"11","author":"SE Venegas-Andraca","year":"2012","unstructured":"Venegas-Andraca, S.E.: Quantum walks: a comprehensive review. Quantum Inf. Process. 11(5), 1015 (2012)","journal-title":"Quantum Inf. Process."},{"issue":"11","key":"2286_CR61","doi-asserted-by":"publisher","first-page":"116001","DOI":"10.1088\/0034-4885\/74\/11\/116001","volume":"74","author":"C Ferrie","year":"2011","unstructured":"Ferrie, C.: Quasi-probability representations of quantum theory with applications to quantum information science. Rep. Prog. Phys. 74(11), 116001 (2011)","journal-title":"Rep. Prog. Phys."},{"issue":"247","key":"2286_CR62","doi-asserted-by":"publisher","first-page":"1417","DOI":"10.1090\/S0025-5718-03-01609-0","volume":"73","author":"B Deconinck","year":"2004","unstructured":"Deconinck, B., Heil, M., Bobenko, A., Van Hoeij, M., Schmies, M.: Computing Riemann theta functions. Math. Comput. 73(247), 1417 (2004)","journal-title":"Math. Comput."},{"key":"2286_CR63","first-page":"101","volume":"54","author":"GFB Riemann","year":"1857","unstructured":"Riemann, G.F.B.: Theorie der Abel\u2019schen functionen. Journal f\u00fcr reine und angewandte Mathematik 54, 101 (1857)","journal-title":"Journal f\u00fcr reine und angewandte Mathematik"},{"key":"2286_CR64","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2843-6","volume-title":"Tata Lectures on Theta. I","author":"D Mumford","year":"1983","unstructured":"Mumford, D.: Tata Lectures on Theta. I. Birkh\u00e4user Boston Inc., Boston (1983)"},{"key":"2286_CR65","unstructured":"Frauendiener, J., Jaber, C., Klein, C.: Efficient computation of multidimensional theta functions. arXiv:1701.07486 (2017)"},{"key":"2286_CR66","volume-title":"Nonlinear Ocean Wave and the Inverse Scattering Transform. International Geophysics Series","author":"AR Osborne","year":"2002","unstructured":"Osborne, A.R.: Nonlinear Ocean Wave and the Inverse Scattering Transform. International Geophysics Series, vol. 97. Academic Press, Oxford (2002)"},{"issue":"12","key":"2286_CR67","doi-asserted-by":"publisher","first-page":"6957","DOI":"10.1109\/TIT.2015.2485944","volume":"61","author":"S Wahls","year":"2015","unstructured":"Wahls, S., Poor, H.V.: Fast numerical nonlinear Fourier transforms. IEEE Trans. Inf. Theory 61(12), 6957 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2286_CR68","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976667","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2010","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2010)"},{"key":"2286_CR69","doi-asserted-by":"publisher","first-page":"1580","DOI":"10.1103\/PhysRevD.46.1580","volume":"46","author":"HF Dowker","year":"1992","unstructured":"Dowker, H.F., Halliwell, J.J.: Quantum mechanics of history: the decoherence functional in quantum mechanics. Phys. Rev. D 46, 1580 (1992)","journal-title":"Phys. Rev. D"},{"key":"2286_CR70","volume-title":"The Fractional Fourier Transform with Applications in Optics and Signal Processing","author":"H Ozaktas","year":"2001","unstructured":"Ozaktas, H., Zalevsky, Z., Kutay, M.A.: The Fractional Fourier Transform with Applications in Optics and Signal Processing. Wiley, Chichester (2001)"},{"key":"2286_CR71","volume-title":"Fundamenta Nova Theoriae Functionum Ellipticarum","author":"CGJ Jacobi","year":"1829","unstructured":"Jacobi, C.G.J.: Fundamenta Nova Theoriae Functionum Ellipticarum. K\u00f6nigsberg, Omaha (1829)"},{"key":"2286_CR72","doi-asserted-by":"crossref","unstructured":"Lagarias, J.C.: The computational complexity of simultaneous diophantine approximation problems. In: IEEE 23rd Annual Symposium on Foundations of Computer Science, p. 32 (1982)","DOI":"10.1109\/SFCS.1982.43"},{"key":"2286_CR73","doi-asserted-by":"publisher","first-page":"505","DOI":"10.2478\/v10178-011-0051-y","volume":"18","author":"TP Zieli\u0144ski","year":"2011","unstructured":"Zieli\u0144ski, T.P., Duda, K.: Frequency and damping estimation methods-an overview. Metrol. Meas. Syst. 18, 505 (2011)","journal-title":"Metrol. Meas. Syst."},{"key":"2286_CR74","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1088\/2058-7058\/11\/3\/32","volume":"11","author":"D DiVincenzo","year":"1998","unstructured":"DiVincenzo, D., Terhal, B.: Decoherence: the obstacle to quantum computation. Phys. World 11, 53 (1998)","journal-title":"Phys. World"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2286-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-019-2286-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2286-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T12:30:37Z","timestamp":1663331437000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-019-2286-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,20]]},"references-count":74,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["2286"],"URL":"https:\/\/doi.org\/10.1007\/s11128-019-2286-6","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2019,4,20]]},"assertion":[{"value":"12 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"167"}}