{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T04:26:55Z","timestamp":1778905615229,"version":"3.51.4"},"reference-count":79,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T00:00:00Z","timestamp":1676937600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"BPI France","award":["Project DOS0148634\/00"],"award-info":[{"award-number":["Project DOS0148634\/00"]}]},{"name":"BPI France","award":["Project DOS0148633\/00"],"award-info":[{"award-number":["Project DOS0148633\/00"]}]},{"DOI":"10.13039\/501100003032","name":"ANRT","doi-asserted-by":"crossref","award":["CIFRE 2022\/0081"],"award-info":[{"award-number":["CIFRE 2022\/0081"]}],"id":[{"id":"10.13039\/501100003032","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"We introduceP<\/mml:mi>e<\/mml:mi>r<\/mml:mi>c<\/mml:mi>e<\/mml:mi>v<\/mml:mi>a<\/mml:mi>l<\/mml:mi><\/mml:math>, an open-source software platform for simulating and interfacing with discrete-variable photonic quantum computers, and describe its main features and components. Its Python front-end allows photonic circuits to be composed from basic photonic building blocks like photon sources, beam splitters, phase-shifters and detectors. A variety of computational back-ends are available and optimised for different use-cases. These use state-of-the-art simulation techniques covering both weak simulation, or sampling, and strong simulation. We give examples ofP<\/mml:mi>e<\/mml:mi>r<\/mml:mi>c<\/mml:mi>e<\/mml:mi>v<\/mml:mi>a<\/mml:mi>l<\/mml:mi><\/mml:math>in action by reproducing a variety of photonic experiments and simulating photonic implementations of a range of quantum algorithms, from Grover's and Shor's to examples of quantum machine learning.P<\/mml:mi>e<\/mml:mi>r<\/mml:mi>c<\/mml:mi>e<\/mml:mi>v<\/mml:mi>a<\/mml:mi>l<\/mml:mi><\/mml:math>is intended to be a useful toolkit for experimentalists wishing to easily model, design, simulate, or optimise a discrete-variable photonic experiment, for theoreticians wishing to design algorithms and applications for discrete-variable photonic quantum computing platforms, and for application designers wishing to evaluate algorithms on available state-of-the-art photonic quantum computers.<\/jats:p>","DOI":"10.22331\/q-2023-02-21-931","type":"journal-article","created":{"date-parts":[[2023,3,18]],"date-time":"2023-03-18T22:08:02Z","timestamp":1679177282000},"page":"931","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":56,"title":["Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing"],"prefix":"10.22331","volume":"7","author":[{"given":"Nicolas","family":"Heurtel","sequence":"first","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"},{"name":"Universit\u00e9 Paris-Saclay, Inria, CNRS, ENS Paris-Saclay, CentraleSup\u00e9lec, LMF, 91190, 15 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Fyrillas","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"},{"name":"Centre for Nanosciences and Nanotechnology, CNRS, Universit\u00e9 Paris-Saclay, UMR 9001, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gr\u00e9goire de","family":"Gliniasty","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rapha\u00ebl","family":"Le Bihan","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00e9bastien","family":"Malherbe","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Physique de l\u2019Ecole Normale Sup\u00e9rieure - PSL, 45 rue d\u2019Ulm, 75230, Paris Cedex 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marceau","family":"Pailhas","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Bertasi","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boris","family":"Bourdoncle","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre-Emmanuel","family":"Emeriau","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rawad","family":"Mezher","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luka","family":"Music","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nadia","family":"Belabas","sequence":"additional","affiliation":[{"name":"Centre for Nanosciences and Nanotechnology, CNRS, Universit\u00e9 Paris-Saclay, UMR 9001, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beno\u00eet","family":"Valiron","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Inria, CNRS, ENS Paris-Saclay, CentraleSup\u00e9lec, LMF, 91190, 15 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascale","family":"Senellart","sequence":"additional","affiliation":[{"name":"Centre for Nanosciences and Nanotechnology, CNRS, Universit\u00e9 Paris-Saclay, UMR 9001, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shane","family":"Mansfield","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean","family":"Senellart","sequence":"additional","affiliation":[{"name":"Quandela, 7 Rue L\u00e9onard de Vinci, 91300 Massy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2023,2,21]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Shor, P., ``Algorithms for quantum computation: discrete logarithms and factoring,'' in Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124\u2013134. IEEE, Nov., 1994.","DOI":"10.1109\/SFCS.1994.365700"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Grover, L.K., ``A fast quantum mechanical algorithm for database search,'' in Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, STOC '96, pp. 212\u2013219. Association for Computing Machinery, July, 1996.","DOI":"10.1145\/237814.237866"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Preskill, J., ``Quantum computing in the NISQ era and beyond,'' Quantum 2, 79 (2018).","DOI":"10.22331\/q-2018-08-06-79"},{"key":"3","unstructured":"Preskill, J., ``Quantum computing and the entanglement frontier,'' arXiv:1203.5813 [quant-ph] (2011)."},{"key":"4","doi-asserted-by":"publisher","unstructured":"Arute, F., Arya, K., Babbush, R., Bacon, D. et al, ``Quantum supremacy using a programmable superconducting processor,'' Nature 574, 505\u2013510 (2019).","DOI":"10.1038\/s41586-019-1666-5"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Zhong, H.S., Wang, H., Deng, Y.H., Chen, M.C. et al, ``Quantum computational advantage using photons,'' Science 370, 1460\u20131463 (2020).","DOI":"10.1126\/science.abe8770"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Wu, Y., Bao, W.S., Cao, S., Chen, F. et al, ``Strong quantum computational advantage using a superconducting quantum processor,'' Physical Review Letters 127, 180501 (2021).","DOI":"10.1103\/PhysRevLett.127.180501"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Zhong, H.S., Deng, Y.H., Qin, J., Wang, H. et al, ``Phase-programmable Gaussian Boson Sampling using stimulated squeezed light,'' Physical Review Letters 127, 180502 (2021). Publisher: American Physical Society.","DOI":"10.1103\/PhysRevLett.127.180502"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Madsen, L.S., Laudenbach, F., Askarani, M.F., Rortais, F. et al, ``Quantum computational advantage with a programmable photonic processor,'' Nature 606, 75\u201381 (2022).","DOI":"10.1038\/s41586-022-04725-x"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Nikolopoulos, G.M. and Brougham, T., ``Decision and function problems based on Boson Sampling,'' Physical Review A 94, 012315 (2016).","DOI":"10.1103\/PhysRevA.94.012315"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Nikolopoulos, G.M., ``Cryptographic One-Way Function based on Boson Sampling,'' Quantum Information Processing 18, 259 (2019).","DOI":"10.1007\/s11128-019-2372-9"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Banchi, L., Fingerhuth, M., Babej, T., Ing, C. and Arrazola, J.M., ``Molecular docking with Gaussian Boson Sampling,'' Science Advances 6, eaax1950 (2020).","DOI":"10.1126\/sciadv.aax1950"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H. et al, ``A variational eigenvalue solver on a photonic quantum processor,'' Nature Communications 5, 4213 (2014).","DOI":"10.1038\/ncomms5213"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Gan, B.Y., Leykam, D. and Angelakis, D.G., ``Fock State-enhanced expressivity of Quantum Machine Learning models,'' in Conference on Lasers and Electro-Optics, p. JW1A.73. Optica Publishing Group, 2021.","DOI":"10.1364\/CLEO_AT.2021.JW1A.73"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Farhi, E., Goldstone, J. and Gutmann, S., ``A Quantum Approximate Optimization Algorithm,'' arXiv:1411.4028 [quant-ph] (2014).","DOI":"10.48550\/arXiv.1411.4028"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Bharti, K., Cervera-Lierta, A., Kyaw, T.H., Haug, T. et al, ``Noisy intermediate-scale quantum algorithms,'' Rev. Mod. Phys. 94, 015004 (2022).","DOI":"10.1103\/RevModPhys.94.015004"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Cao, Y., Romero, J., Olson, J.P., Degroote, M. et al, ``Quantum chemistry in the age of quantum computing,'' Chemical Reviews 119, 10856\u201310915 (2019).","DOI":"10.1021\/acs.chemrev.8b00803"},{"key":"17","doi-asserted-by":"publisher","unstructured":"McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S.C. and Yuan, X., ``Quantum computational chemistry,'' Rev. Mod. Phys. 92, 015003 (2020).","DOI":"10.1103\/RevModPhys.92.015003"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Jiang, Z., Sung, K.J., Kechedzhi, K., Smelyanskiy, V.N. and Boixo, S., ``Quantum algorithms to simulate many-body physics of correlated fermions,'' Phys. Rev. Applied 9, 044036 (2018).","DOI":"10.1103\/PhysRevApplied.9.044036"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Davoudi, Z., Hafezi, M., Monroe, C., Pagano, G. et al, ``Towards analog quantum simulations of lattice gauge theories with trapped ions,'' Phys. Rev. Research 2, 023015 (2020).","DOI":"10.1103\/PhysRevResearch.2.023015"},{"key":"20","doi-asserted-by":"publisher","unstructured":"Vikst\u00e5l, P., Gr\u00f6nkvist, M., Svensson, M., Andersson, M. et al, ``Applying the Quantum Approximate Optimization Algorithm to the tail-assignment problem,'' Phys. Rev. Applied 14, 034009 (2020).","DOI":"10.1103\/PhysRevApplied.14.034009"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Zhu, L., Tang, H.L., Barron, G.S., Calderon-Vargas, F.A. et al, ``An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer,'' arXiv.2005.10258 [quant-ph] (2020).","DOI":"10.48550\/ARXIV.2005.10258"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Schuld, M., Br\u00e1dler, K., Israel, R., Su, D. and Gupt, B., ``Measuring the similarity of graphs with a Gaussian Boson sampler,'' Phys. Rev. A 101, 032314 (2020).","DOI":"10.1103\/PhysRevA.101.032314"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Huang, H.Y., Broughton, M., Cotler, J., Chen, S. et al, ``Quantum advantage in learning from experiments,'' arXiv.2112.00778 [quant-ph] (2021).","DOI":"10.48550\/ARXIV.2112.00778"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Knill, E., Laflamme, R. and Milburn, G.J., ``A scheme for efficient quantum computation with linear optics,'' Nature 409, 46\u201352 (2001).","DOI":"10.1038\/35051009"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Kieling, K., Rudolph, T. and Eisert, J., ``Percolation, renormalization, and quantum computing with nondeterministic gates,'' Physical Review Letters 99, 130501 (2007).","DOI":"10.1103\/PhysRevLett.99.130501"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Bartolucci, S., Birchall, P., Bombin, H., Cable, H. et al, ``Fusion-based quantum computation,'' arXiv:2101.09310 [quant-ph] (2021).","DOI":"10.48550\/arXiv.2101.09310"},{"key":"27","doi-asserted-by":"publisher","unstructured":"Aaronson, S. and Arkhipov, A., ``The computational complexity of linear optics,'' in Proceedings of the forty-third annual ACM symposium on Theory of computing, STOC '11, pp. 333\u2013342. Association for Computing Machinery, June, 2011.","DOI":"10.1145\/1993636.1993682"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Killoran, N., Izaac, J., Quesada, N., Bergholm, V. et al, ``Strawberry Fields: A software platform for photonic quantum computing,'' Quantum 3, 129 (2019).","DOI":"10.22331\/q-2019-03-11-129"},{"key":"29","doi-asserted-by":"publisher","unstructured":"Fingerhuth, M., Babej, T. and Wittek, P., ``Open source software in quantum computing,'' PLOS ONE 13, e0208561 (2018).","DOI":"10.1371\/journal.pone.0208561"},{"key":"30","unstructured":"tA v, A., ANIS, M.S., Abby-Mitchell, Abraham, H. et al, ``Qiskit: An Open-source Framework for Quantum Computing,'' 2021."},{"key":"31","doi-asserted-by":"publisher","unstructured":"Aguado, D.G., Gimeno, V., Moyano-Fern\u00e1ndez, J.J. and Garcia-Escartin, J.C., ``QOptCraft: A Python package for the design and study of linear optical quantum systems,'' arXiv.2108.06186 [quant-ph] (2021).","DOI":"10.48550\/arxiv.2108.06186"},{"key":"32","doi-asserted-by":"publisher","unstructured":"Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C. et al, ``Linear optical quantum computing with photonic qubits,'' Rev. Mod. Phys. 79, 135\u2013174 (2007).","DOI":"10.1103\/RevModPhys.79.135"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Kok, P. and Lovett, B.W., ``Introduction to optical quantum information processing,''. Cambridge University Press, 2010.","DOI":"10.1017\/CBO9781139193658"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Reck, M., Zeilinger, A., Bernstein, H.J. and Bertani, P., ``Experimental realization of any discrete unitary operator,'' Phys. Rev. Lett. 73, 58\u201361 (1994).","DOI":"10.1103\/PhysRevLett.73.58"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Clements, W.R., Humphreys, P.C., Metcalf, B.J., Kolthammer, W.S. and Walmsley, I.A., ``Optimal design for universal multiport interferometers,'' Optica 3, 1460\u20131465 (2016).","DOI":"10.1364\/OPTICA.3.001460"},{"key":"36","doi-asserted-by":"crossref","unstructured":"Chekhova, M. and Banzer, P., ``Polarization of Light: In Classical, Quantum, and Nonlinear Optics,''. De Gruyter, 2021.","DOI":"10.1515\/9783110668025"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Valiant, L.G., ``The complexity of computing the permanent,'' Theoretical Computer Science 8, 189\u2013201 (1979).","DOI":"10.1016\/0304-3975(79)90044-6"},{"key":"38","doi-asserted-by":"publisher","unstructured":"Spedalieri, F., Lee, H., Lee, H., Dowling, J. and Dowling, J., ``Linear optical quantum computing with polarization encoding,'' in Frontiers in Optics (2005), paper LMB4, p. LMB4. Optica Publishing Group, Oct., 2005.","DOI":"10.1364\/LS.2005.LMB4"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Clifford, P. and Clifford, R., ``The classical complexity of Boson Sampling,'' in Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Proceedings, pp. 146\u2013155. Society for Industrial and Applied Mathematics, Jan., 2018.","DOI":"10.1137\/1.9781611975031.10"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Glynn, D.G., ``The permanent of a square matrix,'' European Journal of Combinatorics 31, 1887\u20131891 (2010).","DOI":"10.1016\/j.ejc.2010.01.010"},{"key":"41","doi-asserted-by":"publisher","unstructured":"Clifford, P. and Clifford, R., ``Faster classical Boson Sampling,'' arXiv:2005.04214 [quant-ph] (2020).","DOI":"10.48550\/arXiv.2005.04214"},{"key":"42","doi-asserted-by":"crossref","unstructured":"Ryser, H.J., ``Combinatorial mathematics,'', vol. 14. American Mathematical Society, 1963.","DOI":"10.5948\/UPO9781614440147"},{"key":"43","doi-asserted-by":"publisher","unstructured":"Gupt, B., Izaac, J. and Quesada, N., ``The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling,'' Journal of Open Source Software 4, 1705 (2019).","DOI":"10.21105\/joss.01705"},{"key":"44","doi-asserted-by":"crossref","unstructured":"Heurtel, N., Mansfield, S., Senellart, J. and Valiron, B., ``Strong Simulation of Linear Optical Processes,'' arXiv:2206.10549 [quant-ph] (2022).","DOI":"10.1016\/j.cpc.2023.108848"},{"key":"45","doi-asserted-by":"publisher","unstructured":"Ralph, T.C., Langford, N.K., Bell, T.B. and White, A.G., ``Linear optical controlled-NOT gate in the coincidence basis,'' Physical Review A 65, 062324 (2002).","DOI":"10.1103\/PhysRevA.65.062324"},{"key":"46","doi-asserted-by":"publisher","unstructured":"Hong, C.K., Ou, Z.Y. and Mandel, L., ``Measurement of subpicosecond time intervals between two photons by interference,'' Physical Review Letters 59, 2044\u20132046 (1987). Publisher: American Physical Society.","DOI":"10.1103\/PhysRevLett.59.2044"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Santori, C., Fattal, D., Vu\u010dkovi\u0107, J., Solomon, G.S. and Yamamoto, Y., ``Indistinguishable photons from a single-photon device,'' Nature 419, 594\u2013597 (2002).","DOI":"10.1038\/nature01086"},{"key":"48","doi-asserted-by":"crossref","unstructured":"Giesz, V., Cavity-enhanced photon-photon interactions with bright quantum dot sources. Theses, Universit\u00e9 Paris Saclay (COmUE), Dec., 2015.","DOI":"10.1103\/PhysRevB.92.161302"},{"key":"49","doi-asserted-by":"publisher","unstructured":"Mezher, R. and Mansfield, S., ``Assessing the quality of near-term photonic quantum devices,'' arXiv:2202.04735 [quant-ph] (2022).","DOI":"10.48550\/arXiv.2202.04735"},{"key":"50","doi-asserted-by":"publisher","unstructured":"Brualdi, R.A. and Ryser, H.J., ``Combinatorial Matrix Theory,''. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1991.","DOI":"10.1017\/CBO9781107325708"},{"key":"51","doi-asserted-by":"publisher","unstructured":"Aaronson, S. and Brod, D.J., ``BosonSampling with lost photons,'' Phys. Rev. A 93, 012335 (2016).","DOI":"10.1103\/PhysRevA.93.012335"},{"key":"52","doi-asserted-by":"publisher","unstructured":"Arkhipov, A., ``BosonSampling is robust against small errors in the network matrix,'' Phys. Rev. A 92, 062326 (2015).","DOI":"10.1103\/PhysRevA.92.062326"},{"key":"53","doi-asserted-by":"publisher","unstructured":"Kalai, G. and Kindler, G., ``Gaussian noise sensitivity and Boson Sampling,'' arXiv:1409.3093 [quant-ph] (2014).","DOI":"10.48550\/arXiv.1409.3093"},{"key":"54","doi-asserted-by":"publisher","unstructured":"Russell, N.J., Chakhmakhchyan, L., O'Brien, J.L. and Laing, A., ``Direct dialling of Haar random unitary matrices,'' New Journal of Physics 19, 033007 (2017).","DOI":"10.1088\/1367-2630\/aa60ed"},{"key":"55","doi-asserted-by":"publisher","unstructured":"Wang, H., Qin, J., Ding, X., Chen, M.C. et al, ``Boson Sampling with 20 input photons and a 60-mode interferometer in a $10^{14}$-dimensional Hilbert space,'' Physical Review Letters 123, 250503 (2019).","DOI":"10.1103\/PhysRevLett.123.250503"},{"key":"56","doi-asserted-by":"publisher","unstructured":"Shchesnovich, V.S., ``Universality of generalized bunching and efficient assessment of Boson Sampling,'' Phys. Rev. Lett. 116, 123601 (2016).","DOI":"10.1103\/PhysRevLett.116.123601"},{"key":"57","doi-asserted-by":"publisher","unstructured":"Tichy, M.C., Mayer, K., Buchleitner, A. and M\u00f8lmer, K., ``Stringent and efficient assessment of Boson-Sampling devices,'' Phys. Rev. Lett. 113, 020502 (2014).","DOI":"10.1103\/PhysRevLett.113.020502"},{"key":"58","doi-asserted-by":"publisher","unstructured":"Walschaers, M., Kuipers, J., Urbina, J.D., Mayer, K. et al, ``Statistical benchmark for BosonSampling,'' New Journal of Physics 18, 032001 (2016).","DOI":"10.1088\/1367-2630\/18\/3\/032001"},{"key":"59","doi-asserted-by":"publisher","unstructured":"Roy, T., Jiang, L. and Schuster, D.I., ``Deterministic Grover search with a restricted oracle,'' arXiv:2201.00091 [quant-ph] (2022).","DOI":"10.48550\/arXiv.2201.00091"},{"key":"60","doi-asserted-by":"publisher","unstructured":"Long, G.L., ``Grover algorithm with zero theoretical failure rate,'' Phys. Rev. A 64, 022307 (2001).","DOI":"10.1103\/PhysRevA.64.022307"},{"key":"61","doi-asserted-by":"publisher","unstructured":"Kwiat, P.G., Mitchell, J.R., Schwindt, P.D.D. and White, A.G., ``Grover's search algorithm: An optical approach,'' Journal of Modern Optics 47, 257\u2013266 (2000).","DOI":"10.1080\/09500340008244040"},{"key":"62","doi-asserted-by":"publisher","unstructured":"Rivest, R.L., Shamir, A. and Adleman, L., ``A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,'' Commun. ACM 21, 120\u2013126 (1978).","DOI":"10.1145\/359340.359342"},{"key":"63","doi-asserted-by":"publisher","unstructured":"Politi, A., Matthews, J.C.F. and O'Brien, J.L., ``Shor\u2019s quantum factoring algorithm on a photonic chip,'' Science 325, 1221\u20131221 (2009).","DOI":"10.1126\/science.1173731"},{"key":"64","doi-asserted-by":"publisher","unstructured":"Du, Y., Hsieh, M.H., Liu, T. and Tao, D., ``Expressive power of parametrized quantum circuits,'' Physical Review Research 2, 033125 (2020).","DOI":"10.1103\/PhysRevResearch.2.033125"},{"key":"65","doi-asserted-by":"crossref","unstructured":"Hoeffding, W., ``Probability inequalities for sums of bounded random variables,'' in The collected works of Wassily Hoeffding, pp. 409\u2013426. Springer, 1994.","DOI":"10.1007\/978-1-4612-0865-5_26"},{"key":"66","doi-asserted-by":"publisher","unstructured":"Shadbolt, P.J., Verde, M.R., Peruzzo, A., Politi, A. et al, ``Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,'' Nature Photonics 6, 45\u201349 (2012).","DOI":"10.1038\/nphoton.2011.283"},{"key":"67","doi-asserted-by":"publisher","unstructured":"Nelder, J.A. and Mead, R., ``A Simplex Method for Function Minimization,'' The Computer Journal 7, 308\u2013313 (1965).","DOI":"10.1093\/comjnl\/7.4.308"},{"key":"68","doi-asserted-by":"publisher","unstructured":"O'Malley, P.J.J., Babbush, R., Kivlichan, I.D., Romero, J. et al, ``Scalable quantum simulation of molecular energies,'' Phys. Rev. X 6, 031007 (2016).","DOI":"10.1103\/PhysRevX.6.031007"},{"key":"69","doi-asserted-by":"publisher","unstructured":"Colless, J.I., Ramasesh, V.V., Dahlen, D., Blok, M.S. et al, ``Computation of molecular spectra on a quantum processor with an error-resilient algorithm,'' Phys. Rev. X 8, 011021 (2018).","DOI":"10.1103\/PhysRevX.8.011021"},{"key":"70","doi-asserted-by":"publisher","unstructured":"Harris, C.R., Millman, K.J., van der Walt, S.J., Gommers, R. et al, ``Array programming with NumPy,'' Nature 585, 357\u2013362 (2020).","DOI":"10.1038\/s41586-020-2649-2"},{"key":"71","doi-asserted-by":"publisher","unstructured":"P\u00e9rez-Salinas, A., Cervera-Lierta, A., Gil-Fuster, E. and Latorre, J.I., ``Data re-uploading for a universal quantum classifier,'' Quantum 4, 226 (2020).","DOI":"10.22331\/q-2020-02-06-226"},{"key":"72","doi-asserted-by":"publisher","unstructured":"Schuld, M., Sweke, R. and Meyer, J.J., ``Effect of data encoding on the expressive power of variational quantum-machine-learning models,'' Phys. Rev. A 103, 032430 (2021).","DOI":"10.1103\/PhysRevA.103.032430"},{"key":"73","doi-asserted-by":"publisher","unstructured":"Hadfield, R.H., ``Single-photon detectors for optical quantum information applications,'' Nature Photonics 3, 696\u2013705 (2009).","DOI":"10.1038\/nphoton.2009.230"},{"key":"74","doi-asserted-by":"publisher","unstructured":"Kyriienko, O., Paine, A.E. and Elfving, V.E., ``Solving nonlinear differential equations with differentiable quantum circuits,'' Physical Review A 103, 052416 (2021).","DOI":"10.1103\/PhysRevA.103.052416"},{"key":"75","doi-asserted-by":"publisher","unstructured":"Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M. et al, ``SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,'' Nature Methods 17, 261\u2013272 (2020).","DOI":"10.1038\/s41592-019-0686-2"},{"key":"76","unstructured":"Raschka, S. and Mirjalili, V., ``Python machine learning: Machine learning and deep learning with Python, scikit-learn, and TensorFlow 2,''. Packt Publishing Ltd, 2019."},{"key":"77","unstructured":"Widder, D.V., ``The heat equation,'', vol. 67. Academic Press, 1976."},{"key":"78","unstructured":"Constantin, P. and Foias, C., ``Navier-stokes equations,''. University of Chicago Press, 2020."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2023-02-21-931\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T04:59:51Z","timestamp":1702097991000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2023-02-21-931\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,21]]},"references-count":79,"URL":"https:\/\/doi.org\/10.22331\/q-2023-02-21-931","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,21]]},"article-number":"931"}}