Gaussian boson sampling using threshold detectors
Open accessAbstract
We study what is arguably the most experimentally appealing boson sampling architecture: Gaussian states sampled with threshold detectors. We show that, in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models. We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures. Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all boson sampling models that employ Gaussian states and threshold detectors.
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A simpler form of the GBS experiment where only the presence or absence of photons is detected can be used to sample from the Torontonian function of a matrix.
“A simpler form of the experiment where instead of counting the number of photons in each mode, we only detect if there are photons or not in each mode, can be used to sample from the so-called Torontonian function of a matrix (Quesada et al. , 2018).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Quesada et al., 2018
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Dellios, A. S., Opanchuk, B., Goodman, N., Reid, M. D., & Drummond, P. D. (2025) · Physics Letters A · doi:10.1016/j.physleta.2025.130529 · Cited by 6 · see citing works
Gaussian boson sampling with 1,024 squeezed states in 8,176 modes
Liu, H. C., Su, H., Deng, Y.-H., Gong, S.-Q., Gu, Y.-C., Tang, H., Jia, M.-H., Wei, Q., Song, Y.-K., Wang, D.-Z., et al. (2026) · Nature · doi:10.1038/s41586-026-10523-6 · Cited by 5 · see citing works
Reis, M., & Oliveira, A. C. (2021) · Journal of Computational Electronics · doi:10.1007/s10825-021-01761-0 · Cited by 5 · see citing works
Boost clustering with Gaussian Boson Sampling: a quantum-classical hybrid approach
Bonaldi, N., Rossi, M. S., Mattioli, D., Grapulin, M., Fernandéz, B. S., Caputo, D., Magagnini, M., Osti, A., & Veronese, F. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00185-w · Cited by 5 · see citing works
Boson sampling for generalized bosons
Kuo, E.-J., Xu, Y., Hangleiter, D., Grankin, A., & Hafezi, M. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043096 · Cited by 5 · 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
On Quantum Steering and Wigner Negativity
Walschaers, M. (2023) · Quantum · doi:10.22331/q-2023-06-07-1038 · Cited by 5 · see citing works
A complementary resource relation of concurrence and roughness for a two-qubit state
Reis, M., & Oliveira, A. C. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128313 · Cited by 4 · see citing works
Benchmarking Quantum Computational Advantages on Supercomputers
Wu, J., & Liu, Y. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202400143 · Cited by 4 · see citing works
Training Gaussian boson sampling by quantum machine learning
Conti, C. (2021) · Quantum Machine Intelligence · doi:10.1007/s42484-021-00052-y · Cited by 4 · see citing works
High performance Boson sampling simulation via data-flow engines
Morse, G., Rybotycki, T., Kaposi, Á., Kolarovszki, Z., Stojčić, U., Kozsik, T., Mencer, O., Oszmaniec, M., Zimborás, Z., & Rakyta, P. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad313b · Cited by 4 · see citing works
Classical simulation of bosonic linear-optical random circuits beyond linear light conePreprint
Oh, C., Lim, Y., Fefferman, B., & Jiang, L. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.10083 · Cited by 4 · see citing works
Second moment of Hafnians in Gaussian boson sampling
Ehrenberg, A., Iosue, J. T., Deshpande, A., Hangleiter, D., & Gorshkov, A. V. (2025) · Physical Review A · doi:10.1103/physreva.111.042412 · Cited by 3 · see citing works
Kopylov, D. A., Stefszky, M., Meier, T., Silberhorn, C., & Sharapova, P. R. (2025) · Physical Review Research · doi:10.1103/zp72-7qwl · Cited by 3 · see citing works
Effect of photonic errors on quantum enhanced dense-subgraph finding
Solomons, N. R., Thomas, O., & McCutcheon, D. P. S. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.20.054043 · Cited by 3 · see citing works
Sample efficient graph classification using binary Gaussian boson sampling
Anteneh, A., & Pfister, O. (2023) · Physical Review A · doi:10.1103/physreva.108.062411 · Cited by 3 · see citing works
Gaussian boson sampling at finite temperature
Bressanini, G., Kwon, H., & Kim, M. S. (2024) · Physical Review A · doi:10.1103/physreva.109.013707 · Cited by 3 · see citing works
Gaussian boson sampling with click-counting detectors
Bressanini, G., Kwon, H., & Kim, M. S. (2024) · Physical Review A · doi:10.1103/physreva.109.023708 · Cited by 3 · see citing works
Nonclassicality measures of single-mode quantum states
Oliveira, A. C. (2025) · International Journal of Quantum Information · doi:10.1142/s0219749925300025 · Cited by 3 · see citing works
Post-selection in noisy Gaussian boson sampling: part is better than whole
Yang, T.-Y., Shen, Y.-X., Cao, Z., & Wang, X. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acf06c · Cited by 3 · see citing works
Polynomial speedup in Torontonian calculation by a scalable recursive algorithmPreprint
Kaposi, Á., Kolarovszki, Z., Kozsik, T., Zimborás, Z., & Rakyta, P. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.04528 · Cited by 3 · see citing works
Ultrashort-pulse-pumped, single-mode type-0 squeezers in lithium niobate nanophotonics
Houde, M., Beaudoin, L., Kwolek, R., Hirota, K., Nehra, R., & Quesada, N. (2025) · Optica Quantum · doi:10.1364/opticaq.566703 · Cited by 2 · see citing works
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Simulating Sparse and Shallow Gaussian Boson Sampling
Kolarovszki, Z., Kaposi, Á., Kozsik, T., & Zimborás, Z. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-36030-5_17 · Cited by 2 · see citing works
Resourcefulness of non-classical continuous-variable quantum gates
Frigerio, M., Debray, A., Treps, N., & Walschaers, M. (2026) · Quantum · doi:10.22331/q-2026-07-08-2155 · Cited by 2 · see citing works
Kocharovsky, V. V. (2024) · Entropy · doi:10.3390/e26110926 · Cited by 2 · see citing works
Validation tests of Gaussian boson samplers with photon-number resolving detectors
Dellios, A. S., Reid, M. D., & Drummond, P. D. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/adfe16 · Cited by 2 · see citing works
Boson sampling from non-Gaussian states
Hamilton, C. S., & Jex, I. (2024) · Physical Review A · doi:10.1103/physreva.109.052427 · Cited by 2 · see citing works
Review on quantum advantages of sampling problems
Li, Y., Han, Z.-Y., Li, C.-J., Jin, L., Yuan, X., & Wu, B. (2021) · Acta Physica Sinica · doi:10.7498/aps.70.20211428 · Cited by 2 · see citing works
Proposal for practical multidimensional quantum networks
Bacco, D., Bulmer, J. F. F., Erhard, M., Huber, M., & Paesani, S. (2021) · Physical Review A · doi:10.1103/physreva.104.052618 · Cited by 1 · see citing works
Developing a practical model for noise in entangled-photon detection
Truong, T., Arenz, C., & Lukens, J. M. (2025) · Physical Review A · doi:10.1103/64lg-dwnm · Cited by 1 · see citing works
Noise reduction of multimode Gaussian-boson-sampling circuits via unitary averaging
Swain, S. N., Marshman, R. J., Solntsev, A. S., & Ralph, T. C. (2025) · Physical Review A · doi:10.1103/n9nc-xcmr · Cited by 1 · see citing works
Bianchi, L., Marconi, C., Ares, L., Bacco, D., & Sperling, J. (2025) · Physical Review Research · doi:10.1103/8hy1-m5gg · Cited by 1 · see citing works
Employing Integrated Quantum Photonic Computers for Gaussian Boson Sampling
Ghasemi, M., Kaatuzian, H., Noshad, H., Hassani, M., Motaharifar, M., & NoroozOliaei, M. (2024) · doi:10.1109/icee63041.2024.10667961 · Cited by 1 · see citing works
Conti, C. (2023) · Quantum science and technology · doi:10.1007/978-3-031-44226-1_12 · Cited by 1 · see citing works
- Authors
- Quesada, N., Arrazola, J. M., & Killoran, N.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2018-12-18
- Volume
- 98
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2810513857
- Cited by
- 120
- References
- 33
- Citations by year
- 2026: 6 · 2025: 17 · 2024: 21 · 2023: 22 · 2022: 21 · 2021: 14 · 2020: 12 · 2019: 7
- FWCI
- 4.62
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PolyPublie (École Polytechnique de Montréal) (submittedVersion)
- arXiv (Cornell University)
- 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 Mechanics and Applications
- Keywords
- Gaussian boson sampling, threshold detectors, permanent, hafnian, Gaussian states, photon number statistics
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