Photonic implementation of boson sampling: a review
Open accessAbstract
Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope.
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The approach can represent a promising platform for the implementation of Boson Sampling and Gaussian Boson Sampling experiments in large optical lattices.
“Furthermore, given the possibility to exploit multiphoton inputs and to control the performed transformation, this approach can also represent a promising platform for the implementation of Boson Sampling and Gaussian Boson Sampling experiments in large optical lattices 30 .”
From Quantum walks of two correlated photons in a 2D synthetic lattice (2022) · cites this paper as [30]
Section 4 (Experimental Boson Sampling; page unavailable) reports both boson sampling and Gaussian boson sampling in a chip with an array of 12 coupled waveguides. It also discusses control of optical transformations in other interferometer designs. The review does not establish that the particular approach in the citing sentence can implement both experiments in large optical lattices. (LLM, conf=0.84)
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Lund, A. P., Rahimi-Keshari, S., & Ralph, T. C. (2017) · Physical Review A · doi:10.1103/physreva.96.022301 · Cited by 28 · see citing works
Counting perfect matchings as fast as Ryser
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Many-body quantum interference on hypercubes
Dittel, C., Keil, R., & Weihs, G. (2016) · Quantum Science and Technology · doi:10.1088/2058-9565/aa540c · Cited by 27 · see citing works
Efficient classical simulation of noisy quantum computationPreprint
Gao, X., & Duan, L. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.03176 · Cited by 27 · see citing works
The Classical Complexity of Boson Sampling
Clifford, P., & Raphaël Clifford, A. (2018) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611975031.10 · Cited by 26 · see citing works
Classical benchmarking of Gaussian Boson Sampling on the Titan supercomputer
Gupt, B., Arrazola, J. M., Quesada, N., & Bromley, T. R. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02713-6 · Cited by 23 · see citing works
Complexity of simulating constant-depth BosonSampling
Brod, D. J. (2015) · Physical Review A · doi:10.1103/physreva.91.042316 · Cited by 22 · see citing works
Self-citationOptimal photonic indistinguishability tests in multimode networks
Viggianiello, N., Flamini, F., Bentivegna, M., Spagnolo, N., Crespi, A., Brod, D. J., Galvão, E. F., Osellame, R., & Sciarrino, F. (2018) · 中国科学通报：英文版 · doi:10.1016/j.scib.2018.10.009 · Cited by 22 · see citing works
Self-citationLaibacher, S., & Tamma, V. (2018) · Physical Review A · doi:10.1103/physreva.98.053829 · Cited by 21 · see citing works
Certification of Boson Sampling Devices with Coarse-Grained MeasurementsPreprint
Wang, S.-T., & Duan, L. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1601.02627 · Cited by 15 · see citing works
Algorithms, Probability, Networks, and Games
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Bentivegna, M., Spagnolo, N., & Sciarrino, F. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/4/041001 · Cited by 13 · see citing works
Self-citationDynamical Casimir Effect for Gaussian Boson Sampling
Peropadre, B., Huh, J., & Sabín, C. (2018) · Scientific Reports · doi:10.1038/s41598-018-22086-2 · Cited by 13 · see citing works
A certification scheme for the boson sampler
Liu, K., Lund, A. P., Gu, Y., & Ralph, T. C. (2016) · Journal of the Optical Society of America B · doi:10.1364/josab.33.001835 · Cited by 12 · see citing works
Geometry & Topology Monographs
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Toward quantum computational supremacy of boson sampling with random overlap in the photonic spectraPreprint
Laibacher, S., & Tamma, V. (2018) · arXiv (Cornell University) · Cited by 2 · see citing works
Flagged first, then by citations
6 of the 119 references couldn’t be matched to a known paper.
Research works printed but not linked: 4
- L. Troyansky and N. Tishby, "Permanent uncertainty: on the quantum evaluation of the determinant and the permanent of a matrix," in Proc. Phys. Comp., pp. 1-5 (1996).
- Ernesto F. Galvão received his PhD from the University of Oxford, UK, in 2002. He was a postdoctoral fellow in the Perimeter Institute until 2005 and has been a professor in the Physics Institute of the Universidade Federal Fluminense since 2006. His research interests include quantum computation and information, as well as foundations of quantum mechanics.
- Nicolò Spagnolo received his PhD in 2012 in physical science of matter, with a thesis on experimental multiphoton quantum optical states. He is a temporary researcher in the Department of Physics of Sapienza Università di Roma. His research interests have been focused on quan- tum information and simulation protocols employing different photonic platforms. These research activities include the implementation of boson sampling instances and of validation protocols with integrated photonics and quantum phase estimation experiments.
- Fabio Sciarrino received his PhD in 2004 with a thesis in experimental quantum optics. He is a full professor and head of the Quantum Information Lab in the Department of Physics of Sapienza Università di Roma. Since 2013, he has been a fellow of the Sapienza School for Advanced Studies. His main field of research is quantum information and quantum optics, with works on quantum teleportation, optimal quan- tum machines, fundamental tests, quantum communication, and orbital angular momentum.
Cited by
Sorted by citations
Photonic quantum information processing: a concise review
Slussarenko, S., & Pryde, G. J. (2019) · Applied Physics Reviews · doi:10.1063/1.5115814 · Cited by 644 · see citing works
Wang, H., Qin, J., Ding, X., Chen, M.-C., Chen, S., You, X., He, Y., Jiang, X. Q., You, L., Wang, Z., et al. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.250503 · Cited by 499 · see citing works
Hybrid integration methods for on-chip quantum photonics
Kim, J.-H., Aghaeimeibodi, S., Carolan, J., Englund, D., & Waks, E. (2020) · Optica · doi:10.1364/optica.384118 · Cited by 272 · see citing works
Two-photon interference: the Hong–Ou–Mandel effect
Bouchard, F., Sit, A., Zhang, Y., Fickler, R., Miatto, F. M., Yao, Y., Sciarrino, F., & Karimi, E. (2020) · Reports on Progress in Physics · doi:10.1088/1361-6633/abcd7a · Cited by 217 · see citing works
Self-citationApplications of single photons to quantum communication and computing
Couteau, C., Barz, S., Durt, T., Gerrits, T., Huwer, J., Prevedel, R., Rarity, J., Shields, A., & Weihs, G. (2023) · Nature Reviews Physics · doi:10.1038/s42254-023-00583-2 · Cited by 216 · see citing works
“Another approach to information processing with photonic systems is boson sampling 185,186 .”
BackgroundSingle-photon sources: approaching the ideal through multiplexing
Meyer-Scott, E., Silberhorn, C., & Migdall, A. (2020) · Review of Scientific Instruments · doi:10.1063/5.0003320 · Cited by 204 · see citing works
Tan, D., Wang, Z., Xu, B., & Qiu, J. (2021) · Advanced Photonics · doi:10.1117/1.ap.3.2.024002 · Cited by 188 · see citing works
Quantum dots for photonic quantum information technology
Heindel, T., Kim, J., Gregersen, N., Rastelli, A., & Reitzenstein, S. (2023) · Advances in Optics and Photonics · doi:10.1364/aop.490091 · Cited by 179 · see citing works
Computational advantage of quantum random sampling
Hangleiter, D., & Eisert, J. (2023) · Reviews of Modern Physics · doi:10.1103/revmodphys.95.035001 · Cited by 145 · see citing works
Femtosecond laser micromachining for integrated quantum photonics
Corrielli, G., Crespi, A., & Osellame, R. (2021) · Nanophotonics · doi:10.1515/nanoph-2021-0419 · Cited by 125 · see citing works
Self-citationUltra-low loss quantum photonic circuits integrated with single quantum emitters
Chanana, A., Larocque, H., Moreira, R. L., Carolan, J., Guha, B., de Melo, E. G., Anant, V., Song, J. D., Englund, D., Blumenthal, D. J., et al. (2022) · Nature Communications · doi:10.1038/s41467-022-35332-z · Cited by 119 · see citing works
“…losses will likely be critical for fault-tolerant photonic computing where photons must be ’stored’ in delay lines 12 , and also for quantum simulation schemes that rely on time-demultiplexing or buffering of single-photons, such as time-bin 13 or high-dimensional Gaussian Boson Sampling 14 .”
Advances in Silicon Quantum Photonics
Adcock, J. C., Bao, J., Chi, Y., Chen, X., Bacco, D., Gong, Q., Oxenløwe, L. K., Wang, J., & Ding, Y. (2020) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/jstqe.2020.3025737 · Cited by 87 · see citing works
“increased HOM visibilities effectively allow larger numbers of photons to interfere [180], for example in boson sampling [181].”
BackgroundNanowire‐based integrated photonics for quantum information and quantum sensing
Chang, J., Gao, J., Zadeh, I. E., Elshaari, A. W., & Zwiller, V. (2023) · Nanophotonics · doi:10.1515/nanoph-2022-0652 · Cited by 74 · see citing works
“With the increase of photon numbers, the task becomes intractable using the classical computation approach due to the intrinsic hardness of calculating the matrix permanent, and thus is considered an excellent candidate to demonstrate quantum computational advantage [98].”
MethodTailoring solid-state single-photon sources with stimulated emissions
Wei, Y., Liu, S., Li, X., Yu, Y., Su, X., Li, S., Shang, X., Liu, H., Hao, H., Ni, H., et al. (2022) · Nature Nanotechnology · doi:10.1038/s41565-022-01092-6 · Cited by 69 · see citing works
Split-ring polariton condensates as macroscopic two-level quantum systems
Xue, Y., Chestnov, I. Y., Sedov, E., Kiktenko, E. O., Fedorov, A. K., Schumacher, S., Ma, X., & Kavokin, A. V. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013099 · Cited by 59 · see citing works
Quantum light in complex media and its applications
Lib, O., & Bromberg, Y. (2022) · Nature Physics · doi:10.1038/s41567-022-01692-y · Cited by 60 · see citing works
Scalable and programmable phononic network with trapped ions
Chen, W., Lu, Y., Zhang, S., Zhang, K., Huang, G., Qiao, M., Su, X., Zhang, J., Zhang, J.-N., Banchi, L., et al. (2023) · Nature Physics · doi:10.1038/s41567-023-01952-5 · Cited by 54 · see citing works
“The network has been implemented mostly in optical systems with photons [11].”
BackgroundIntegrated photonics in quantum technologies
Giordani, T., Hoch, F., Carvacho, G., Spagnolo, N., & Sciarrino, F. (2023) · Rivista Del Nuovo Cimento · doi:10.1007/s40766-023-00040-x · Cited by 54 · see citing works
Self-citationReconfigurable continuously-coupled 3D photonic circuit for Boson Sampling experiments
Hoch, F., Piacentini, S., Giordani, T., Tian, Z.-N., Iuliano, M., Esposito, C., Camillini, A., Carvacho, G., Ceccarelli, F., Spagnolo, N., et al. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00568-6 · Cited by 51 · see citing works
Self-citationEpitaxial quantum dots: a semiconductor launchpad for photonic quantum technologies
Zhou, X., Zhai, L., & Liu, J. (2022) · Photonics Insights · doi:10.3788/pi.2022.r07 · Cited by 50 · see citing works
“Photonic boson sampling [318] describes a sampling task of the photon distribution of identical photons after multiple mutual interferences.”
BackgroundA universal programmable Gaussian boson sampler for drug discovery
Yu, S., Zhong, Z., Fang, Y., Patel, R. B., Li, Q., Liu, W., Li, Z., Xu, L., Sagona-Stophel, S., Mer, E., et al. (2023) · Nature Computational Science · doi:10.1038/s43588-023-00526-y · Cited by 52 · see citing works
Programmable high-dimensional Hamiltonian in a photonic waveguide array
Yang, Y., Chapman, R. J., Haylock, B., Lenzini, F., Joglekar, Y. N., Lobino, M., & Peruzzo, A. (2024) · Nature Communications · doi:10.1038/s41467-023-44185-z · Cited by 49 · see citing works
“This corresponds to a different pattern of voltages which needs to be applied on the device.”
BackgroundOszmaniec, M., Dangniam, N., Morales, M. E. S., & Zimborás, Z. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020328 · Cited by 43 · see citing works
“The first column lists the different sampling schemes: Random Circuit Sampling (RCS) [12, 13, 22, 47–49], Boson Sampling (BS) [9, 25, 26, 50], Gaussian Boson Sampling (GBS) [17, 27, 51, 52], Instantaneous Quantum Polynomial (IQP) [11, 53] and Fermion Sampling.”
BackgroundClassical simulation of linear optics subject to nonuniform losses
Brod, D. J., & Oszmaniec, M. (2020) · Quantum · doi:10.22331/q-2020-05-14-267 · Cited by 43 · see citing works
“also benefits from the technology and expertise developed by the quantum optics community in the last decades [3].”
BackgroundSelf-citationQuantifying n -Photon Indistinguishability with a Cyclic Integrated Interferometer
Pont, M., Albiero, R., Thomas, S. E., Spagnolo, N., Ceccarelli, F., Corrielli, G., Brieussel, A., Somaschi, N., Huet, H., Harouri, A., et al. (2022) · Physical Review X · doi:10.1103/physrevx.12.031033 · Cited by 41 · see citing works
Self-citationUltra-long quantum walks via spin-orbit photonics
Colandrea, F. D., Babazadeh, A., Dauphin, A., Massignan, P., Marrucci, L., & Cardano, F. (2022) · Optica · doi:10.1364/optica.474542 · Cited by 31 · see citing works
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
Self-citationRivera, N., Sloan, J., Salamin, Y., Joannopoulos, J. D., & Marin Soljacic, A. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2219208120 · Cited by 34 · see citing works
Efficient verification of boson sampling
Chabaud, U., Grosshans, F., Kashefi, E., & Markham, D. (2021) · Quantum · doi:10.22331/q-2021-11-15-578 · Cited by 37 · see citing works
“However, there is no efficient verification protocol using single-mode Gaussian state preparation nor single-mode Gaussian measurements for Boson Sampling with input single photons: current methods used for the validation of Boson sampling are either not scalable or only provide partial certificates on the tested prob…”
MethodGu, X., Chen, L., & Krenn, M. (2020) · Physical Review A · doi:10.1103/physreva.101.033816 · Cited by 32 · see citing works
Fock state-enhanced expressivity of quantum machine learning models
Gan, B. Y., Leykam, D., & Angelakis, D. G. (2022) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-022-00135-0 · Cited by 33 · see citing works
“Our proposed architecture can be implemented with current technology, such as integrated photonic circuits used for boson sampling experiments [7].”
MethodAn Application of Quantum Annealing Computing to Seismic Inversion
Souza, A. M., Martins, E. O., Roditi, I., Sá, N., Sarthour, R. S., & Oliveira, I. S. (2022) · Frontiers in Physics · doi:10.3389/fphy.2021.748285 · Cited by 30 · see citing works
“The Canadian company D-Wave, leader in the computational model known as quantum annealing [6], is already trading quantum machines, and the also Canadian Xanadu is providing cloud access to their photonic quantum computer [7, 8].”
BackgroundHigh-Performance Reservoir Computing With Fluctuations in Linear Networks
Nokkala, J., Martínez‐Peña, R., Zambrini, R., & Soriano, M. C. (2021) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2021.3105695 · Cited by 30 · see citing works
Experimental quantification of four-photon indistinguishability
Giordani, T., Brod, D. J., Esposito, C., Viggianiello, N., Romano, M., Flamini, F., Carvacho, G., Spagnolo, N., Galvão, E. F., & Sciarrino, F. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab7a30 · Cited by 27 · see citing works
Self-citationMetasurface quantum graphs for generalized Hong-Ou-Mandel interference
Yousef, K. M. A., D’Alessandro, M., Yeh, M., Sinclair, N. E., Lončar, M., & Capasso, F. (2025) · Science · doi:10.1126/science.adw8404 · Cited by 26 · see citing works
Nonlinear Quantum Photonics With AlGaAs Bragg-Reflection Waveguides
Appas, F., Meskine, O., Lemaître, A., Morassi, M., Baboux, F., Amanti, M. I., & Ducci, S. (2022) · Journal of Lightwave Technology · doi:10.1109/jlt.2022.3214466 · Cited by 26 · see citing works
“Indistinguishable photons are a crucial resource for a large variety of quantum information protocols including long distance quantum communications [50], linear optical quantum computing [51], photonic boson sampling [52] and quantum metrology [53].”
BackgroundInformation processing at the speed of light
AbuGhanem, M. (2024) · Frontiers of Optoelectronics · doi:10.1007/s12200-024-00133-3 · Cited by 26 · see citing works
Spagnolo, N., Brod, D. J., Galvão, E. F., & Sciarrino, F. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00676-x · Cited by 26 · see citing works
Self-citationDynamical learning of a photonics quantum-state engineering process
Suprano, A., Zia, D., Polino, E., Giordani, T., Innocenti, L., Ferraro, A., Paternostro, M., Spagnolo, N., & Sciarrino, F. (2021) · Advanced Photonics · doi:10.1117/1.ap.3.6.066002 · Cited by 20 · see citing works
Self-citationSolid‐state single‐photon sources operating in the telecom wavelength range
Holewa, P., Reiserer, A., Heindel, T., Sanguinetti, S., Huck, A., & Semenova, E. S. (2025) · Nanophotonics · doi:10.1515/nanoph-2024-0747 · Cited by 20 · see citing works
“In boson sampling, the probability distribution of scattered indistinguishable photons is modeled in a linear interferometer [372] requiring much less quantum resources than universal quantum computers.”
Kernel method based on non-linear coherent states in quantum feature space
Tiwari, P., Dehdashti, S., Obeid, A. K., Marttinen, P., & Bruza, P. (2022) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac818e · Cited by 20 · see citing works
Engineering quantum states from a spatially structured quantum eraser
Schiano, C., Sephton, B., Aiello, R. G., Graffitti, F., Lal, N., Chiuri, A., Santoro, S., Amato, L. S., Marrucci, L., de Lisio, C., et al. (2024) · Science Advances · doi:10.1126/sciadv.adm9278 · Cited by 19 · see citing works
Witnesses of coherence and dimension from multiphoton indistinguishability tests
Giordani, T., Esposito, C., Hoch, F., Carvacho, G., Brod, D. J., Galvão, E. F., Spagnolo, N., & Sciarrino, F. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023031 · Cited by 18 · see citing works
“Interestingly, an intermediate model of quantum computation was proposed that only uses the interference of multiple single-photons in a multimode, linear interferometer [36, 37].”
BackgroundSelf-citationProgrammable multiphoton quantum interference in a single spatial mode
Carosini, L., Oddi, V., Giorgino, F., Hansen, L. M., Seron, B., Piacentini, S., Guggemos, T., Agresti, I., Loredo, J. C., & Walther, P. J. (2024) · Science Advances · doi:10.1126/sciadv.adj0993 · Cited by 17 · see citing works
Integrated quantum polariton interferometry
Nigro, D., D’Ambrosio, V., Sanvitto, D., & Gerace, D. (2022) · Communications Physics · doi:10.1038/s42005-022-00810-9 · Cited by 17 · see citing works
Accelerating quantum optics experiments with statistical learning
Cortes, C. L., Adhikari, S., Ma, X., & Gray, S. K. (2020) · Applied Physics Letters · doi:10.1063/1.5143786 · Cited by 16 · see citing works
“[16] Daniel J Brod, Ernesto F Galvão, Andrea Crespi, Roberto Osellame, Nicolò Spagnolo, and Fabio Sciarrino, “Photonic implementation of boson sampling: a review,” Advanced Photonics 1, 034001 (2019).”
BackgroundQuantum Information with Integrated Photonics
Piergentili, P., Amanti, F., Andrini, G., Armani, F., Bellani, V., Bonaiuto, V., Cammarata, S., Campostrini, M., Cornia, S., Dao, T. H., et al. (2023) · Applied Sciences · doi:10.3390/app14010387 · Cited by 14 · see citing works
“Indeed, any experimental instance approaching the regime of quantum advantage must be necessarily accompanied by appropriate evidence that the employed device is correctly performing the sampling process [20,60].”
Variational approach to photonic quantum circuits via the parameter shift rule
Hoch, F., Rodari, G., Giordani, T., Perret, P., Spagnolo, N., Carvacho, G., Pentangelo, C., Piacentini, S., Crespi, A., Ceccarelli, F., et al. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023227 · Cited by 14 · see citing works
“Finally, we define the scattering matrix M associated with the input and output states ⃗r and ⃗s as the N × N matrix defined as The probability to obtain the output state ⃗s from the input state ⃗r can be computed as [33]: where Per ( M ) is the permanent of the scattering matrix M .”
Self-citationLarge reconfigurable quantum circuits with SPAD arrays and multimode fibers
Makowski, A., Dąbrowski, M., Antolović, I. M., Bruschini, C. E., Defienne, H., Edoardo Charbon, A., Łapkiewicz, R., & Gigan, S. (2023) · Optica · doi:10.1364/optica.506943 · Cited by 13 · see citing works
Intense Squeezed Light from Lasers with Sharply Nonlinear Gain at Optical Frequencies
Nguyen, L., Sloan, J., Rivera, N., & Marin Soljacic, A. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.173801 · Cited by 12 · see citing works
SiN integrated photonic components in the visible to near-infrared spectral region
Sanna, M., Baldazzi, A., Piccoli, G., Azzini, S., Ghulinyan, M., & Pavesi, L. (2024) · Optics Express · doi:10.1364/oe.514505 · Cited by 14 · see citing works
“Another example is that of Boson Samplers integrated in the direct-laser written glass platform, which allows demonstrating the ability of photonic structures to perform computational tasks beyond classical capabilities [14,15].”
BackgroundQuantum circuit mapping for universal and scalable computing in MZI-based integrated photonics
Kwon, Y. S., Baldazzi, A., Pavesi, L., & Choi, B.-S. (2024) · Optics Express · doi:10.1364/oe.520492 · Cited by 12 · see citing works
Lee, J.-M., Baldazzi, A., Sanna, M., Azzini, S., Ahn, J. T., Lee, M., Sohn, Y.-I., & Pavesi, L. (2023) · Photonics Research · doi:10.1364/prj.489869 · Cited by 12 · see citing works
“On the other hand,in applications like Boson Sampling [51,52], where a large number of single (heralded) photons is required and the probability to inject a single photon state is proportional to the purity, one needs high values of purity.”
BackgroundEfficient high-fidelity flying qubit shaping
Tissot, B., & Burkard, G. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013150 · Cited by 11 · see citing works
“Additionally, single-photon emission represents a cornerstone for several photonic technologies [11–15].”
BackgroundOn-chip tunable quantum interference in a lithium niobate-on-insulator photonic integrated circuit
Maeder, A., Finco, G., Kaufmann, F., Sabatti, A., Kellner, J., Chapman, R. J., & Grange, R. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad4b98 · Cited by 11 · see citing works
Towards interpretable quantum machine learning via single-photon quantum walks
Flamini, F., Krumm, M., Fiderer, L. J., Müller, T., & Briegel, H. J. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad5907 · Cited by 11 · see citing works
“The impact of imperfections can be estimated using the shared package [17].”
On-chip high-dimensional entangled photon sources
Kaur, T., Peace, D., & Romero, J. (2024) · Journal of Optics · doi:10.1088/2040-8986/ada0c5 · Cited by 11 · see citing works
“A four-photon polarisation-encoded quantum states created via degenerate SFWM within a spiralled Si waveguide in Sagnac configuration has been demonstrated [47], achieving a detection rate of 0.34 Hz at a modest pump power of 600 mW and a fidelity of 0.78 ± 0.02.”
InfluentialPhoton antibunching in single‐molecule vibrational sum‐frequency generation
Kalarde, F. M., Ciccarello, F., Muñoz, C. S., Feist, J., & Galland, C. (2025) · Nanophotonics · doi:10.1515/nanoph-2024-0469 · Cited by 11 · see citing works
“…picosecond relaxation times of vibrational excitations, promises a valuable tool for the production of indistinguishable single photons at THz repetition rates, enabling a breadth of applications such as the realisation of multi-photon entanglement in boson sampling [45] and cluster states [46–49].”
BackgroundWang, X., Zhu, Y., Jin, T., Ou, W., Ou, X., & Zhang, J. (2022) · Chip · doi:10.1016/j.chip.2022.100018 · Cited by 11 · see citing works
Recent progress and applications of III–V quantum dots in quantum technologies
Ma, Z., Wu, S., Li, H., Chen, X., Peng, K., Qian, C., Jin, K., Gong, Q., & Xu, X. (2026) · Applied Physics Reviews · doi:10.1063/5.0291094 · Cited by 10 · see citing works
Semi-Device-Independent Characterization of Multiphoton Indistinguishability
Rodari, G., Novo, L., Albiero, R., Suprano, A., Tavares, C., Caruccio, E., Hoch, F., Giordani, T., Carvacho, G., Gardina, M., et al. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.020340 · Cited by 10 · see citing works
Self-citationQuantum supremacy and quantum phase transitions
Thanasilp, S., Tangpanitanon, J., Lemonde, M.-A., Dangniam, N., & Angelakis, D. G. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.165132 · Cited by 10 · see citing works
Lal, N., Mishra, S., & Singh, R. P. (2022) · AVS Quantum Science · doi:10.1116/5.0083968 · Cited by 10 · see citing works
Atomic boson sampling in a Bose-Einstein-condensed gas
Kocharovsky, V. V., Kocharovsky, V. V., & Tarasov, S. V. (2022) · Physical Review A · doi:10.1103/physreva.106.063312 · Cited by 10 · see citing works
Spectral single photons characterization using generalized Hong–Ou–Mandel interferometry
Fabre, N. (2022) · Journal of Modern Optics · doi:10.1080/09500340.2022.2073613 · Cited by 9 · see citing works
“Discrete variables encoding of single photons have been used in many quantum protocols and the most recent achievements are the experimental realization of boson sampling [3, 4] and in quantum communication protocols [5].”
MethodApplications of the Lambert–Tsallis Wq function in quantum photonic Gaussian boson sampling
Mendes, F. V., Lima, C., & Ramos, R. V. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03559-w · Cited by 9 · see citing works
Certification of Gaussian Boson Sampling via graphs feature vectors and kernels
Giordani, T., Mannucci, V., Spagnolo, N., Fumero, M., Rampini, A., Rodolà, E., & Sciarrino, F. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac969b · Cited by 9 · see citing works
“The BS paradigm corresponds to sampling from the output distribution of a Fock state with n indistinguishable photons after the evolution through a linear optical m-port interferometer [6, 7].”
Self-citationUniversal Time-Dependent Control Scheme for Realizing Arbitrary Linear Bosonic Transformations
Xiang, Z.-L., Olivares, D. G., García‐Ripoll, J. J., & Rabl, P. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.050801 · Cited by 9 · see citing works
Phase-space negativity as a computational resource for quantum kernel methods
Chabaud, U., Ghobadi, R., Beigi, S., & Rahimi-Keshari, S. (2024) · Quantum · doi:10.22331/q-2024-11-07-1519 · Cited by 9 · see citing works
Validating multi-photon quantum interference with finite data
Flamini, F., Walschaers, M., Spagnolo, N., Wiebe, N., Buchleitner, A., & Sciarrino, F. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/aba03a · Cited by 9 · see citing works
Self-citationConfigurable heralded two-photon Fock-states on a chip
Hua, X., Lunghi, T., Doutre, F., Vergyris, P., Sauder, G., Charlier, P., Labonté, L., D’Auria, V., Martin, A., Tascu, S., et al. (2020) · Optics Express · doi:10.1364/oe.403552 · Cited by 9 · see citing works
Multiparameter estimation for qubit states with collective measurements: a case study
Len, Y. L. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac599d · Cited by 9 · see citing works
“identity in boson sampling [87, 88], finding a transformation U that has output signatures that are different for each j-eigenspace, which now includes also inputs of different α, is even harder as N gets larger.”
BackgroundMulti-Qubit Bose–Einstein Condensate Trap for Atomic Boson Sampling
Tarasov, S. V., Shannon, W., Kocharovsky, V. V., & Kocharovsky, V. V. (2022) · Entropy · doi:10.3390/e24121771 · Cited by 9 · see citing works
Generalized interference of fermions and bosons
Spivak, D., Niu, M. Y., Sanders, B. C., & de Guise, H. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023013 · Cited by 8 · see citing works
“Both quantum annealing [60] and boson sampling [8, 61] are examples of specialized, purposed quantum computing that is not universal.”
BackgroundRealization of photon correlations beyond the linear optics limit
Park, G., Matsumoto, I., Kiyohara, T., Hofmann, H. F., Okamoto, R., & Takeuchi, S. (2023) · Science Advances · doi:10.1126/sciadv.adj8146 · Cited by 8 · see citing works
“The combination of single-photon inputs with linear optics transformations has been a workhorse for exploring quantum information science, such as quantum computing ( 3 – 10 ), quantum communication ( 11 – 14 ), and quantum metrology ( 15 , 16 ).”
BackgroundDistinguishability in quantum interference with multimode squeezed states
Shchesnovich, V. S. (2022) · Physical Review A · doi:10.1103/physreva.105.063703 · Cited by 8 · see citing works
“Quantum optical platforms seem to be the most suitable for this purpose [6].”
BackgroundFitzke, E., Niederschuh, F., & Walther, T. (2023) · APL Photonics · doi:10.1063/5.0129638 · Cited by 7 · see citing works
Canonical Resonant Four-Wave-Mixing in Photonic Crystal Cavities : tuning, tolerances and scaling
Chopin, A., Marty, G., Ghorbel, I., Moille, G. T., Martin, A., Combrié, S., Raineri, F., & Rossi, A. D. (2022) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/jstqe.2022.3229164 · Cited by 7 · see citing works
“sources of squeezed light [14], [15], [16], combined with a full photonic circuit [17] are used in Gaussian Boson Sampling [18], a practical configuration to demonstrate quantum advantage in”
MethodHardware requirements for realizing a quantum advantage with deterministic single-photon sources
Sund, P. I., Uppu, R., Paesani, S., & Lodahl, P. (2024) · Physical Review A · doi:10.1103/physreva.109.042613 · Cited by 7 · see citing works
“validating that the samples are produced from the exact distribution, one verifies that the outputs are not reproduced by a computationally efficient distribution [14, 25].”
BackgroundInfluentialIntegration of germanium-vacancy single photon emitters arrays in diamond nanopillars
Redolfi, E., Pugliese, V., Scattolo, E., Cian, A., Missale, E., de Oliveira, F. F., Seniutinas, G., Tchernij, S. D., Dell’Anna, R., Traina, P., et al. (2025) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-025-00329-2 · Cited by 6 · see citing works
“Furthermore, Fock states can be used for implementing boson sampling [13] and for the generation of other more exotic states of light such as Schrödinger cat states [14].”
Complexity-Theoretic Foundations of BosonSampling with a Linear Number of Modes
Bouland, A., Brod, D. J., Datta, I., Fefferman, B., Grier, D., Hernández, F., & Oszmaniec, M. (2026) · Physical Review X · doi:10.1103/xc7b-sjm5 · Cited by 5 · see citing works
Self-citationBoson sampling with ultracold atoms in a programmable optical lattice
Robens, C., Arrazola, Í., Alt, W., Meschede, D., Lamata, L., Solano, E., & Alberti, A. (2024) · Physical Review A · doi:10.1103/physreva.110.012615 · Cited by 7 · see citing works
“A number of experiments have been reported demonstrating boson sampling in photonic quantum circuits [59–70], with the current record being N = 20 photons in M = 60 modes [71].”
BackgroundHybrid Source of Quantum Light for Generation of Frequency Tunable Fock States
Krstić, A., Tiwari, P., Höhe, F., Setzpfandt, F., Peschel, U., Ankerhold, J., & Saravi, S. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.203605 · Cited by 5 · see citing works
Complementary properties of multiphoton quantum states in linear optics networks
Wu, J.-Y., & Murao, M. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abb964 · Cited by 4 · see citing works
Towards the Simplest Model of Quantum Supremacy: Atomic Boson Sampling in a Box Trap
Kocharovsky, V. V., Kocharovsky, V. V., Shannon, W., & Tarasov, S. V. (2023) · Entropy · doi:10.3390/e25121584 · Cited by 5 · see citing works
“…of atoms, equilibrium, and an absence of external sources of bosons, the proposed atomic boson sampling has substantially different physics compared to photonic boson sampling in a linear interferometer, widely studied in the last decade, both theoretically [2–4,11–28] and experimentally [5,29–35].”
BackgroundLavie, E., Primaatmaja, I. W., Kon, W. Y., Wang, C., & Lim, C. C. W. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.16.034020 · Cited by 5 · see citing works
“A good example is boson-sampling—a type of non-universal quantum computation [11, 12].”
BackgroundUniversal multi-port interferometers with minimal optical depthPreprint
Pereira, L., Rojas, A. J., Cañas, G., Lima, G., Delgado, A., & Cabello, A. (2020) · arXiv (Cornell University) · Cited by 5 · see citing works
Kundu, S., Szuniewicz, J., Firlik, G., Krupiński‐Ptaszek, A., & Łapkiewicz, R. (2024) · Optica Quantum · doi:10.1364/opticaq.522894 · Cited by 4 · see citing works
Kovalyuk, V. V., Венедиктов, И. О., Седых, К. О., Svyatodukh, S., Hydyrova, S., Moiseev, K. M., Florya, I., Prokhodtsov, A. I., Galanova, V. S., Kobtsev, D. A., et al. (2024) · Radiophysics and Quantum Electronics · doi:10.1007/s11141-024-10340-9 · Cited by 4 · see citing works
Sengupta, K., Dinesh, S., Shafi, K., Asokan, S., & Chandrashekar, C. M. (2024) · Physical Review Applied · doi:10.1103/r7yp-1vz4 · Cited by 17 · see citing works
Scalable multiphoton generation from cavity-synchronized single-photon sources
Li, M., García‐Ripoll, J. J., & Ramos, T. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033295 · Cited by 4 · see citing works
“In the short-term, the implementation of our scheme can already enable quantum advantage experiments with hundreds of microwave photons such as boson sampling [18] or quantum metrology [16, 17].”
BackgroundObservation of Extrinsic Topological Phases in Floquet Photonic Lattices
Asapanna, R., Sokhen, R. E., Adiyatullin, A. F., Hainaut, C., Delplace, P., Gómez-León, Á., & Amo, A. (2025) · Physical Review Letters · doi:10.1103/tqyx-qyj4 · Cited by 4 · see citing works
Jia, S.-C. (2023) · Highlights in Science Engineering and Technology · doi:10.54097/hset.v38i.5873 · Cited by 3 · see citing works
Coherence via reiterated beam splitting
Díez, G., Ares, L., & Luis, A. (2024) · Physical Review A · doi:10.1103/physreva.109.063706 · Cited by 3 · see citing works
Transition of Anticoncentration in Gaussian Boson Sampling
Ehrenberg, A., Iosue, J. T., Deshpande, A., Hangleiter, D., & Gorshkov, A. V. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.140601 · Cited by 3 · see citing works
Entanglement in the full state vector of boson sampling
Qiao, Y., Huh, J., & Großmann, F. (2023) · SciPost Physics · doi:10.21468/scipostphys.15.1.007 · Cited by 3 · see citing works
“A review of the many different variants of boson sampling and their experimental realization as well as its validation, including references to pioneering studies, is given in [5].”
BackgroundMethodKiyohara, T., Okamoto, R., & Takeuchi, S. (2020) · Optics Express · doi:10.1364/oe.393584 · Cited by 3 · see citing works
Young, S. M., & Soh, D. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013130 · Cited by 2 · see citing works
Multiphoton, multimode state classification for nonlinear optical circuits
Kopylov, D. A., Offen, C., Ares, L., Wembe, B., Ober‐Blöbaum, S., Meier, T., Sharapova, P. R., & Sperling, J. (2025) · Physical Review Research · doi:10.1103/sv6z-v1gk · Cited by 2 · see citing works
“Already the states in the base class [1 N ] M appear in different, pioneering topics in quantum optics and quantum technologies, such as boson sampling [7] and quantum walks [9].”
Observation of Lie algebraic invariants in quantum linear optics
Rodari, G., Francalanci, T., Caruccio, E., Hoch, F., Carvacho, G., Giordani, T., Spagnolo, N., Albiero, R., Giano, N. D., Ceccarelli, F., et al. (2025) · Physical Review Research · doi:10.1103/7961-hg2q · Cited by 2 · see citing works
Self-citation
- Authors
- Brod, D. J., Galvão, E. F., Crespi, A., Osellame, R., Spagnolo, N., & Sciarrino, F.
- Affiliations
- Universidade Federal Fluminense (BR)
- Istituto di Fotonica e Nanotecnologie (IT)
- Sapienza University of Rome (IT)
- ORCID
- Venue
- Advanced Photonics
- Publisher
- SPIE-Intl Soc Optical Eng
- Published
- 2019-05-09
- Volume
- 1
- Issue
- 03
- Pages
- 1-14
- ISSN
- 2577-5421 (ISSN-L)
- OpenAlex
- W2954967660
- Cited by
- 159
- References
- 119
- Citations by year
- 2026: 12 · 2025: 25 · 2024: 30 · 2023: 25 · 2022: 28 · 2021: 17 · 2020: 18 · 2019: 4
- FWCI
- 7.73
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- Advanced Photonics (publishedVersion, cc-by)
- Virtual Community of Pathological Anatomy (University of Castilla La Mancha) (submittedVersion, other-oa)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion, cc-by)
- Funders
- Conselho Nacional de Desenvolvimento Científico e Tecnológico (731473)
- QuantERA (731473)
- Horizon 2020 Framework Programme (742745, 731473, 641039, H2020-FETPROACT-2014)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- boson sampling, quantum advantage, linear interferometer, single photons, photodetection
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