arxiv: 2604.15258 · v1 · submitted 2026-04-16 · 🪐 quant-ph

Recognition: unknown

General framework for anticoncentration and linear cross-entropy benchmarking in photonic quantum advantage experiments

\'Agoston Kaposi, Micha{\l} Oszmaniec, Zolt\'an Kolarovszki, Zolt\'an Zimbor\'as

Authors on Pith no claims yet

Pith reviewed 2026-05-10 11:37 UTC · model grok-4.3

classification 🪐 quant-ph

keywords linear cross-entropy benchmarkingBoson Samplinganticoncentrationrepresentation theoryphotonic quantum computingGaussian Boson SamplingHaar random interferometerssymmetric representations

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The pith

A representation-theoretic framework computes average linear cross-entropy benchmarking scores and proves anticoncentration for Fock-state Boson Sampling in the saturated regime.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a general method based on representation theory to calculate average linear cross-entropy benchmarking scores for experiments that scatter photons through random optical interferometers. This covers both standard Boson Sampling with Fock states and Gaussian Boson Sampling, and works whether the number of photons is much smaller or comparable to the number of modes. Using the same techniques, the authors show that the output probability distribution anticoncentrates in the saturated regime for traditional Boson Sampling. However, for Gaussian Boson Sampling the second-moment analysis falls short of proving a useful anticoncentration bound. The approach highlights how entanglement between photons influences these benchmarking and concentration properties.

Core claim

By decomposing two copies of the symmetric n-particle bosonic space into irreducible representations of the unitary group U(m), two-copy averages over Haar-random interferometers reduce to the computation of purities of the initial state after tracing out some particles. This allows exact classical evaluation of average LXEB scores across photonic quantum advantage protocols in any regime, including the saturated one where photon and mode numbers are comparable. The same reduction establishes anticoncentration of the output distribution for Fock-state Boson Sampling when the system is saturated.

What carries the argument

Decomposition of two copies of the n-particle bosonic space Sym^n(C^m) into irreducible representations of U(m), reducing two-copy Haar averages to purities of initial states after partial traces over particles.

If this is right

Average LXEB scores can be computed exactly for n-photon m-mode scattering experiments in any regime.
Anticoncentration of the output distribution holds for traditional Fock-state Boson Sampling when photon number approaches mode number.
Second moments are insufficient to establish meaningful anticoncentration for Gaussian Boson Sampling.
Particle entanglement after partial traces directly determines the benchmarking scores and concentration properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The symmetry reduction could be adapted to compute higher moments or design optimized initial states for stronger verification in photonic experiments.
Similar decomposition techniques might apply to other random unitary sampling models where multiple copies of symmetric spaces appear.
Tuning the entanglement structure of the input state could improve LXEB scores or anticoncentration bounds in practice.

Load-bearing premise

The two-copy bosonic space decomposes into U(m) irreps such that Haar averages reduce exactly to purities after partial traces without additional corrections in the saturated regime.

What would settle it

A direct numerical computation of the second moment of output probabilities for small n and m in the saturated regime that deviates from the purity value predicted by the irrep decomposition would disprove the reduction.

Figures

Figures reproduced from arXiv: 2604.15258 by \'Agoston Kaposi, Micha{\l} Oszmaniec, Zolt\'an Kolarovszki, Zolt\'an Zimbor\'as.

**Figure 2.** Figure 2: FIG. 2. Algorithmic workflow for computing the LXEB reference value. Starting from the problem parameters [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Comparison of analytical and estimated LXEB reference values. For each value of [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. LXEB fidelity in lossy Gaussian Boson Sampling. Exact LXEB fidelities are shown as a function of the number of [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Numerical values of [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗

read the original abstract

Photonic architectures are one of the leading platforms for demonstrating quantum computational advantage, with Boson Sampling and Gaussian Boson Sampling as the primary schemes. Yet, we lack for these photonic primitives a systematic theoretical understanding of linear cross-entropy benchmarking (LXEB), which is a central tool for testing quantum advantage proposals. In this work, we develop a representation-theoretic framework for the classical computation of average LXEB scores and second moments of output probability distributions, covering a range of quantum advantage experiments based on scattering $n$-photon states through $m$-mode Haar-random interferometers. Our methods apply in any regime, including the saturated regime, where the (expected) number of photons is comparable to the number of optical modes. The same second-moment techniques also allow us to prove anticoncentration for traditional Fock-state Boson Sampling in the saturated regime. Interestingly, for Gaussian Boson Sampling second moments are not sufficient to establish a meaningful anticoncentration statement. The technical core of our approach rests on decomposing two copies of the $n$-particle bosonic space $\mathrm{Sym}^n(\mathbb{C}^m)$ into irreducible representations of $\mathrm{U}(m)$. This reduces two-copy Haar averages to computing purities of initial states after partial traces over particles, highlighting the role that particle entanglement plays for LXEB and anticoncentration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a representation-theoretic reduction that computes average LXEB scores and proves anticoncentration for Fock-state Boson Sampling in the saturated regime, but the exactness of that reduction when n approaches m needs direct verification.

read the letter

The core contribution is a decomposition of the two-copy space Sym^n(C^m) ⊗ Sym^n(C^m) under the diagonal U(m) action. This turns Haar averages of LXEB scores and output second moments into purities of the initial state after partial traces over particles. The same technique yields an anticoncentration proof for ordinary Boson Sampling even when photon number is comparable to mode number. For Gaussian Boson Sampling the second-moment calculation shows why anticoncentration does not follow in the same way. Both results apply across regimes without the usual restrictions on n and m. That is the actual advance: a uniform method that was not available from prior work on these benchmarks. The approach is grounded in standard facts about symmetric representations, so the formal steps look reproducible once the derivations are checked. It also makes explicit that particle entanglement enters the LXEB and anticoncentration expressions through those purities. This is useful for anyone who needs to benchmark or analyze photonic experiments with concrete formulas rather than sampling. The main question is whether the partial-trace operators commute cleanly with the symmetrizer when occupation numbers become order one. If higher-weight representations contribute extra overlap terms in the saturated regime, the claimed closed forms would acquire correction factors. The abstract states the reduction is exact, so the paper must show that no such terms arise. Minor additional checks on boundary cases and error propagation would strengthen the claims. The work is aimed at groups doing photonic quantum advantage experiments or theoretical analysis of their statistics. It deserves a serious referee because the method is general, the gap it fills is real, and the results are falsifiable once the derivations are on the table. I would send it for review.

Referee Report

1 major / 0 minor

Summary. The manuscript develops a representation-theoretic framework for computing average linear cross-entropy benchmarking (LXEB) scores and second moments of output probability distributions for photonic quantum advantage experiments based on scattering n-photon states through m-mode Haar-random interferometers. The core technique decomposes the two-copy bosonic space Sym^n(C^m) ⊗ Sym^n(C^m) under the diagonal U(m) action, reducing Haar averages to purities of initial states after partial traces over particles. This applies in any regime, including the saturated regime n ≈ m. The same methods prove anticoncentration for traditional Fock-state Boson Sampling in the saturated regime, while showing that second moments are insufficient to establish meaningful anticoncentration for Gaussian Boson Sampling.

Significance. If the central reduction holds exactly, the work supplies a systematic, closed-form tool for classically evaluating LXEB and output statistics in photonic advantage proposals across all parameter regimes, which is directly relevant to experimental verification. The anticoncentration result for Fock-state Boson Sampling in the saturated regime addresses a technically demanding case using standard U(m) representation theory on bosonic spaces. The framework explicitly connects particle entanglement (via the partial traces) to these benchmarking quantities, providing insight beyond case-by-case calculations.

major comments (1)

[Technical core / decomposition of two-copy bosonic space] The technical core (abstract and the decomposition of Sym^n(C^m) ⊗ Sym^n(C^m)) asserts that two-copy Haar averages reduce exactly to purities after partial traces over particles, with no additional corrections even in the saturated regime n ≈ m. However, when occupation numbers become O(1), the partial-trace operators may fail to commute with the bosonic symmetrizer, potentially introducing overlaps with higher-weight representations and correction factors. This would undermine the claimed closed-form LXEB expressions and the anticoncentration proof for Fock-state sampling. An explicit check, commutation verification, or error bound for n ≈ m is required.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need to confirm the exactness of the central decomposition in the saturated regime. We address this point directly below.

read point-by-point responses

Referee: The technical core (abstract and the decomposition of Sym^n(C^m) ⊗ Sym^n(C^m)) asserts that two-copy Haar averages reduce exactly to purities after partial traces over particles, with no additional corrections even in the saturated regime n ≈ m. However, when occupation numbers become O(1), the partial-trace operators may fail to commute with the bosonic symmetrizer, potentially introducing overlaps with higher-weight representations and correction factors. This would undermine the claimed closed-form LXEB expressions and the anticoncentration proof for Fock-state sampling. An explicit check, commutation verification, or error bound for n ≈ m is required.

Authors: We thank the referee for this observation. The decomposition of the two-copy space Sym^n(C^m) ⊗ Sym^n(C^m) under the diagonal U(m) action is an exact statement of representation theory that holds for arbitrary n and m (including n ≈ m) without qualification or correction terms. The partial-trace operators employed in the framework are fully symmetric with respect to particle exchange and therefore commute with the bosonic symmetrizer by construction; they map the symmetric subspace to itself and do not mix in higher-weight representations. Consequently, the reduction of two-copy Haar averages to purities of the partially traced states remains exact in every regime, including the saturated case. This exact reduction directly supports both the closed-form LXEB expressions and the anticoncentration argument for Fock-state Boson Sampling. To make the commutation explicit, we will add a short verification (for example, the n = m = 3 case) in the revised manuscript. revision: partial

Circularity Check

0 steps flagged

No circularity: standard representation-theoretic reduction applied to bosonic space

full rationale

The paper's derivation chain rests on decomposing Sym^n(C^m) ⊗ Sym^n(C^m) under the diagonal U(m) action to reduce two-copy Haar averages exactly to purities after partial traces. This is a direct, non-self-referential application of known facts from representation theory of unitary groups to the bosonic Hilbert space, as described in the abstract. No equations or claims reduce a 'prediction' or central result to a fitted parameter, self-definition, or load-bearing self-citation chain. The framework is self-contained against external mathematical benchmarks (Schur-Weyl duality, irrep decompositions) and does not rename known empirical patterns or smuggle ansatzes via prior work. Minor self-citations, if present, are not load-bearing for the LXEB or anticoncentration results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard assumptions from quantum optics and representation theory with no free parameters or new entities introduced in the abstract.

axioms (2)

domain assumption Interferometers are drawn from the Haar measure on U(m)
Standard modeling choice for random linear optical networks in Boson Sampling literature.
standard math The two-copy space Sym^n(C^m) ⊗ Sym^n(C^m) decomposes into U(m) irreps allowing reduction of Haar averages to partial-trace purities
Follows from the representation theory of the unitary group on symmetric spaces.

pith-pipeline@v0.9.0 · 5559 in / 1372 out tokens · 60383 ms · 2026-05-10T11:37:44.972088+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

112 extracted references · 30 canonical work pages

[1]

J. L. O’Brien, A. Furusawa, and J. Vučković, Pho- tonicquantumtechnologies,NaturePhotonics3,687–695 (2009)

2009
[2]

Flamini, N

F. Flamini, N. Spagnolo, N. Viggianiello, A. Crespi, R. Osellame, and F. Sciarrino, Benchmarking integrated linear-optical architectures for quantum information pro- cessing,ScientificReports7,10.1038/s41598-017-15174-2 (2017)

work page doi:10.1038/s41598-017-15174-2 2017
[3]

J. Bao, Z. Fu, T. Pramanik, J. Mao, Y. Chi, Y. Cao, C. Zhai, Y. Mao, T. Dai, X. Chen, X. Jia, L. Zhao, Y. Zheng, B. Tang, Z. Li, J. Luo, W. Wang, Y. Yang, Y. Peng, D. Liu, D. Dai, Q. He, A. L. Muthali, L. K. Oxenløwe, C. Vigliar, S. Paesani, H. Hou, R. Santagati, J. W. Silverstone, A. Laing, M. G. Thompson, J. L. O’Brien, Y. Ding, Q. Gong, and J. Wang, Ve...

2023
[4]

Aaronson and A

S. Aaronson and A. Arkhipov, The computational com- plexity of linear optics, inProceedings of the Forty- Third Annual ACM Symposium on Theory of Comput- ing, STOC ’11 (Association for Computing Machinery, New York, NY, USA, 2011) p. 333–342

2011
[5]

C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Gaussian Boson Sampling, Phys. Rev. Lett.119, 170501 (2017)

2017
[6]

Kruse, C

R. Kruse, C. S. Hamilton, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Detailed study of Gaussian boson sampling, Phys. Rev. A100, 032326 (2019)

2019
[7]

H. Wang, Y. He, Y.-H. Li, Z.-E. Su, b. li, H.-L. Huang, X. Ding, M.-c. Chen, C. Liu, J. Qin, J.-P. Li, Y.-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. Höfling, C.-Y. Lu, and J.-W. Pan, High-efficiency multiphoton boson sampling, Nat. Photon.11(2017)

2017
[8]

D. J. Brod, E. F. Galvão, A. Crespi, R. Osellame, N. Spagnolo, and F. Sciarrino, Photonic implementation of boson sampling: a review, Adv. Photonics1, 1 (2019)

2019
[9]

H. Wang, J. Qin, X. Ding, M.-C. Chen, S. Chen, X. You, Y.-M. He, X. Jiang, L. You, Z. Wang, C. Schneider, J. J. Renema, S. Höfling, C.-Y. Lu, and J.-W. Pan, Boson Sampling with 20 Input Photons and a 60-Mode Interfer- ometer in a1014-Dimensional Hilbert Space, Phys. Rev. Lett.123, 250503 (2019)

2019
[10]

A. W. Young, S. Geller, W. J. Eckner, N. Schine, S. Glancy, E. Knill, and A. M. Kaufman, An atomic bo- son sampler, Nature629, 311–316 (2024)

2024
[11]

Zhong, H

H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, 22 G. Yang, L. You, Z. Wang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Quantum computational advantage using photons, Science370, 1460–1463 (2020)

2020
[12]

Vincent, J

L.S.Madsen, F.Laudenbach, M.F.Askarani, F.Rortais, T. Vincent, J. F. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, A. Lita, T. Gerrits, S. Nam, V. Vaidya, and M. M. et al., Quantum computational ad- vantagewithaprogrammablephotonicprocessor,Nature 606, 75 (2022)

2022
[13]

H.-L. Liu, H. Su, S.-Q. Gong, Y.-C. Gu, H.-Y. Tang, M.-H. Jia, Q. Wei, Y. Song, D. Wang, M. Zheng, F. Chen, L. Li, S. Ren, X. Zhu, M. Wang, Y. Chen, Y. Liu, L. Song, P. Yang, J. Chen, H. An, L. Zhang, L. Gan, G. Yang, J.-M. Xu, Y.-M. He, H. Wang, H.-S. Zhong, M.-C. Chen, X. Jiang, L. Li, N.-L. Liu, Y.-H. Deng, X.-L. Su, Q. Zhang, C.-Y. Lu, and J.-W. Pan, ...

work page arXiv 2025
[14]

Rahimi-Keshari, T

S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves, Suf- ficient Conditions for Efficient Classical Simulation of Quantum Optics, Phys. Rev. X6, 021039 (2016)

2016
[15]

Oszmaniec and D

M. Oszmaniec and D. J. Brod, Classical simulation of photonic linear optics with lost particles, New J. Phys. 20, 092002 (2018)

2018
[16]

García-Patrón, J

R. García-Patrón, J. J. Renema, and V. Shchesnovich, Simulating boson sampling in lossy architectures, Quan- tum3, 169 (2019)

2019
[17]

H. Qi, D. J. Brod, N. Quesada, and R. García-Patrón, Regimes of classical simulability for noisy gaussian boson sampling, Phys. Rev. Lett.124, 100502 (2020)

2020
[18]

V. S. Shchesnovich, Tight bound on the trace distance between a realistic device with partially indistinguishable bosons and the ideal BosonSampling, Phys. Rev. A91, 063842 (2015)

2015
[19]

Renema, A

J. Renema, A. Menssen, W. Clements, G. Triginer, W. Kolthammer, and I. Walmsley, Efficient Classi- cal Algorithm for Boson Sampling with Partially Dis- tinguishable Photons, Physical Review Letters120, 10.1103/physrevlett.120.220502 (2018)

work page doi:10.1103/physrevlett.120.220502 2018
[20]

G. V. Resta, L. Stasi, M. Perrenoud, S. El-Khoury, T. Brydges, R. Thew, H. Zbinden, and F. Bussières, Gigahertz detection rates and dynamic photon-number resolution with superconducting nanowire arrays, Nano Lett.23, 6018 (2023)

2023
[21]

Arkhipov, BosonSampling is robust against small er- rors in the network matrix, Phys

A. Arkhipov, BosonSampling is robust against small er- rors in the network matrix, Phys. Rev. A92, 062326 (2015)

2015
[22]

C. Oh, M. Liu, Y. Alexeev, B. Fefferman, and L. Jiang, Classical algorithm for simulating experimental Gaus- sian boson sampling, Nature Physics20, 1461 (2024), arXiv:2306.03709 [quant-ph]

work page arXiv 2024
[23]

T. Dodd, J. Martínez-Cifuentes, O. T. Brown, N. Que- sada, and R. García-Patrón, A fast and frugal Gaus- sian Boson Sampling emulator (2025), arXiv:2511.14923 [quant-ph]

work page arXiv 2025
[24]

Spagnolo, C

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ram- poni, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, Experimental validation of photonic boson sampling, Nat. Photon.8, 615–620 (2014)

2014
[25]

Eisert, D

J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Quantum certi- fication and benchmarking, Nat. Rev. Phys.2, 382–390 (2020)

2020
[26]

Hangleiter and J

D. Hangleiter and J. Eisert, Computational advantage of quantum random sampling, Rev. Mod. Phys.95, 10.1103/revmodphys.95.035001 (2023)

work page doi:10.1103/revmodphys.95.035001 2023
[27]

Quantum Supremacy

D. Hangleiter, M. Kliesch, J. Eisert, and C. Gogolin, Sample Complexity of Device-Independently Certi- fied “Quantum Supremacy”, Phys. Rev. Lett.122, 10.1103/physrevlett.122.210502 (2019)

work page doi:10.1103/physrevlett.122.210502 2019
[28]

Movassagh, Quantum supremacy and random circuits (2020), arXiv:1909.06210 [quant-ph]

R. Movassagh, Quantum supremacy and random circuits (2020), arXiv:1909.06210 [quant-ph]

work page arXiv 2020
[29]

Bouland, B

A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani, On the complexity and verification of quantum random circuit sampling, Nature Physics15, 159 (2019)

2019
[30]

Bouland, D

A. Bouland, D. Brod, I. Datta, B. Fefferman, D. Grier, F. Hernandez, and M. Oszmaniec, Complexity-theoretic foundations of bosonsampling with a linear number of modes (2025), arXiv:2312.00286 [quant-ph]

work page arXiv 2025
[31]

Oszmaniec, N

M. Oszmaniec, N. Dangniam, M. E. Morales, and Z. Zimborás, Fermion Sampling: A Robust Quantum Computational Advantage Scheme Using Fermionic Lin- ear Optics and Magic Input States, PRX Quantum3, 10.1103/prxquantum.3.020328 (2022)

work page doi:10.1103/prxquantum.3.020328 2022
[32]

Boixo, S

S. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, Characterizing quantum supremacy in near- term devices, Nature Physics14, 595 (2018)

2018
[33]

Aruteet al., Quantum supremacy using a pro- grammable superconducting processor, Nature574, 505–510 (2019)

F. Aruteet al., Quantum supremacy using a pro- grammable superconducting processor, Nature574, 505–510 (2019)

2019
[34]

Aaronson and S

S. Aaronson and S. Gunn, On the classical hardness of spoofing linear cross-entropy benchmarking, Theory of Computing16, 1 (2020)

2020
[35]

Wu, W.-S

Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen, X.Chen, T.-H.Chung, H.Deng, Y.Du, D.Fan, M.Gong, C. Guo, C. Guo, S. Guo, L. Han, L. Hong, H.-L. Huang, Y.-H. Huo, L. Li, N. Li, S. Li, F. Liang, C. Lin, J. Lin, H. Qian, D. Qiao, H. Rong, H. Su, L. Sun, L. Wang, S. Wang, D. Wu, Y. Xu, K. Yan, W. Yang, Y. Yang, Y. Ye, J. Yin, C. Ying, J. Yu, C. Zha, C. Zhang, ...

2021
[36]

Morvanet al., Phase transitions in random circuit sampling, Nature634, 328 (2024)

A. Morvanet al., Phase transitions in random circuit sampling, Nature634, 328 (2024)

2024
[37]

Spoofing linear cross- entropy benchmarking in shallow quantum circuits,

B. Barak, C.-N. Chou, and X. Gao, Spoofing Linear Cross-Entropy Benchmarking in Shallow Quantum Cir- cuits, in12th Innovations in Theoretical Computer Sci- ence Conference (ITCS 2021), LIPIcs, Vol. 185 (Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2021) pp. 30:1–30:20, arXiv:2005.02421 [quant-ph]

work page arXiv 2021
[38]

Aharonov, X

D. Aharonov, X. Gao, Z. Landau, Y. Liu, and U. Vazi- rani, A polynomial-time classical algorithm for noisy ran- dom circuit sampling, inProceedings of the 55th Annual ACM Symposium on Theory of Computing(2023) pp. 945–957, arXiv:2211.03999 [quant-ph]

work page arXiv 2023
[39]

X. Gao, M. Kalinowski, C.-N. Chou, M. D. Lukin, B. Barak, and S. Choi, Limitations of Linear Cross- Entropy as a Measure for Quantum Advantage, PRX Quantum5, 10.1103/prxquantum.5.010334 (2024)

work page doi:10.1103/prxquantum.5.010334 2024
[40]

Martínez-Cifuentes, H

J. Martínez-Cifuentes, H. de Guise, and N. Quesada, Lin- ear Cross-Entropy Certification of Quantum Computa- tional Advantage in Gaussian Boson Sampling (2024), arXiv:2403.15339 [quant-ph]. 23

work page arXiv 2024
[41]

Ehrenberg, J

A. Ehrenberg, J. T. Iosue, A. Deshpande, D. Hangleiter, and A. V. Gorshkov, Transition of Anticoncentration in Gaussian Boson Sampling, Physical Review Letters134, 10.1103/physrevlett.134.140601 (2025)

work page doi:10.1103/physrevlett.134.140601 2025
[42]

Bentivegna, N

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, Experimental scattershot boson sampling, Sci. Adv.1, 10.1126/sciadv.1400255 (2015)

work page doi:10.1126/sciadv.1400255 2015
[43]

Z. Li, N. R. Solomons, J. F. F. Bulmer, R. B. Patel, and I. A. Walmsley, A complexity transition in displaced Gaussian Boson sampling, npj Quantum Inf.11, 119 (2025)

2025
[44]

J. J. Renema, Simulability of partially distinguishable superposition and Gaussian boson sampling, Phys. Rev. A101, 10.1103/physreva.101.063840 (2020)

work page doi:10.1103/physreva.101.063840 2020
[45]

Ehrenberg, J

A. Ehrenberg, J. T. Iosue, A. Deshpande, D. Hangleiter, and A. V. Gorshkov, Second moment of Hafnians in Gaussian boson sampling, Physical Review A111, 10.1103/physreva.111.042412 (2025)

work page doi:10.1103/physreva.111.042412 2025
[46]

L. Stockmeyer, The complexity of approximate count- ing, inProceedings of the Fifteenth Annual ACM Sympo- sium on Theory of Computing, STOC ’83 (Association for Computing Machinery, New York, NY, USA, 1983) p. 118–126

1983
[47]

Nezami, Permanent of random matrices from rep- resentation theory: moments, numerics, concentration, and comments on hardness of boson-sampling (2021), arXiv:2104.06423 [quant-ph]

S. Nezami, Permanent of random matrices from rep- resentation theory: moments, numerics, concentration, and comments on hardness of boson-sampling (2021), arXiv:2104.06423 [quant-ph]

work page arXiv 2021
[48]

M. J. Bremner, A. Montanaro, and D. J. Shep- herd, Achieving quantum supremacy with sparse and noisy commuting quantum computations, Quantum1, 8 (2017)

2017
[49]

Hangleiter, J

D. Hangleiter, J. Bermejo-Vega, M. Schwarz, and J. Eis- ert, Anticoncentration theorems for schemes showing a quantum speedup, Quantum2, 65 (2018)

2018
[50]

A. M. Dalzell, N. Hunter-Jones, and F. G. S. L. Brandão, Random Quantum Circuits Anticoncentrate in Log Depth, PRX Quantum3, 010333 (2022)

2022
[51]

Oszmaniec, R

M. Oszmaniec, R. Augusiak, C. Gogolin, J. Kołodyński, A. Acín, and M. Lewenstein, Random Bosonic States for Robust Quantum Metrology, Physical Review X6, 10.1103/physrevx.6.041044 (2016)

work page doi:10.1103/physrevx.6.041044 2016
[52]

Popkov, M

V. Popkov, M. Salerno, and G. Schütz, Entangling power of permutation-invariant quantum states, Physical Re- view A72, 10.1103/physreva.72.032327 (2005)

work page doi:10.1103/physreva.72.032327 2005
[53]

J. A. Carrasco, F. Finkel, A. González-López, M. A. Rodríguez, and P. Tempesta, Generalized isotropic lip- kin–meshkov–glick models: ground state entanglement and quantum entropies, Journal of Statistical Mechan- ics: Theory and Experiment2016, 033114 (2016)

2016
[54]

Aaronson and A

S. Aaronson and A. Arkhipov, BosonSampling is far from uniform (2013), arXiv:1309.7460 [quant-ph]

work page arXiv 2013
[55]

Spagnolo, C

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ram- poni, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, Experimental validation of photonic boson sampling, Nature Photonics8, 615 (2014)

2014
[56]

Lootens, C

M. Arienzo, D. Grinko, M. Kliesch, and M. Hein- rich, Bosonic Randomized Benchmarking with Passive Transformations, PRX Quantum6, 10.1103/prxquan- tum.6.020305 (2025)

work page doi:10.1103/prxquan- 2025
[57]

C. H. Valahu, T. Navickas, M. J. Biercuk, and T. R. Tan, Benchmarking Bosonic Modes for Quantum Infor- mation with Randomized Displacements, PRX Quantum 5, 10.1103/prxquantum.5.040337 (2024)

work page doi:10.1103/prxquantum.5.040337 2024
[58]

Bentivegna, N

M. Bentivegna, N. Spagnolo, C. Vitelli, D. J. Brod, A. Crespi, F. Flamini, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, Bayesian approach to Boson sampling validation, International Journal of Quantum Information12, 1560028 (2014), https://doi.org/10.1142/S021974991560028X

work page doi:10.1142/s021974991560028x 2014
[59]

Martínez-Cifuentes, K

J. Martínez-Cifuentes, K. M. Fonseca-Romero, and N. Quesada, Classical models may be a better explana- tion of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model, Quantum7, 1076 (2023)

2023
[60]

Laing and J

A. Laing and J. L. O’Brien, Super-stable tomography of any linear optical device (2012), arXiv:1208.2868 [quant- ph]

work page arXiv 2012
[61]

Walschaers, J

M. Walschaers, J. Kuipers, J.-D. Urbina, K. Mayer, M. C. Tichy, K. Richter, and A. Buchleitner, A statistical benchmark for BosonSampling, New Journal of Physics 18, 032001 (2016)

2016
[62]

D. S. Phillips, M. Walschaers, J. J. Renema, I. A. Walms- ley, N. Treps, and J. Sperling, Benchmarking of Gaussian boson sampling using two-point correlators, Physical Re- view A99, 023836 (2019)

2019
[63]

Rahimi-Keshari, T

S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves, Suffi- cient conditions for efficient classical simulation of quan- tum optics, Physical Review X6, 021039 (2016)

2016
[64]

Agresti, N

I. Agresti, N. Viggianiello, F. Flamini, N. Spagnolo, A. Crespi, R. Osellame, N. Wiebe, and F. Sciarrino, Pat- tern recognition techniques for Boson Sampling valida- tion, Physical Review X9, 011013 (2019)

2019
[65]

Seron, L

B. Seron, L. Novo, A. Arkhipov, and N. J. Cerf, Effi- cient validation of Boson Sampling from binned photon- number distributions, Quantum8, 1479 (2024)

2024
[66]

Chabaud, F

U. Chabaud, F. Grosshans, E. Kashefi, and D. Markham, Efficient verification of Boson Sampling, Quantum5, 578 (2021)

2021
[67]

A. M. Dalzell, N. Hunter-Jones, and F. G. S. L. Brandão, Random quantum circuits transform local noise into global white noise, Communications in Mathematical Physics405, 78 (2024)

2024
[68]

Fefferman, S

B. Fefferman, S. Ghosh, M. Gullans, K. Kuroiwa, and K. Sharma, Effect of nonunital noise on random-circuit sampling, PRX Quantum5, 030317 (2024)

2024
[69]

Helsen, I

J. Helsen, I. Roth, E. Onorati, A. H. Werner, and J. Eis- ert, A general framework for randomized benchmarking, PRX Quantum3, 020357 (2022)

2022
[70]

F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki, Local random quantum circuits are approximate polynomial-designs, Communications in Mathematical Physics346, 397 (2016)

2016
[71]

Schuster, J

T. Schuster, J. Haferkamp, and H.-Y. Huang, Ran- dom unitaries in extremely low depth, arXiv preprint arXiv:2407.07754 10.48550/arXiv.2407.07754 (2024)

work page doi:10.48550/arxiv.2407.07754 2024
[72]

R. I. Nepomechie and D. Raveh, Qudit Dicke state prepa- ration, Quantum Information & Computation24, 37–56 (2024)

2024
[73]

Fulton and J

W. Fulton and J. Harris,Representation Theory: A First Course, Graduate Texts in Mathematics (Springer New York, Springer New York, NY, 1991)

1991
[74]

Grier, D

D. Grier, D. J. Brod, J. M. Arrazola, M. B. d. A. Alonso, and N. Quesada, The Complexity of Bipartite Gaussian Boson Sampling, Quantum6, 863 (2022)

2022
[75]

A. A. Mele, Introduction to Haar Measure Tools in Quan- tum Information: A Beginner’s Tutorial, Quantum8, 24 1340 (2024)

2024
[76]

Kolarovszki, T

Z. Kolarovszki, T. Rybotycki, P. Rakyta, A. Kaposi, B. Poór, S. Jóczik, D. T. R. Nagy, H. Varga, K. H. El- Safty, G. Morse, M. Oszmaniec, T. Kozsik, and Z. Zim- borás, Piquasso: A Photonic Quantum Computer Simu- lation Software Platform, Quantum9, 1708 (2025)

2025
[77]

V. V. Petrov, On lower bounds for tail probabilities, Journal of Statistical Planning and Inference137, 2703 (2007), 5th St. Petersburg Workshop on Simulation

2007
[78]

Quesada, J

N. Quesada, J. M. Arrazola, and N. Killoran, Gaussian boson sampling using threshold detectors, Physical Re- view A98, 10.1103/physreva.98.062322 (2018)

work page doi:10.1103/physreva.98.062322 2018
[79]

F.H.B.SomhorstandJ.J.Renema,Mitigatingquantum operation infidelity through engineering the distribution of photon losses, Optica Quantum4, 130 (2026)

2026
[80]

Hunter-Jones and J

N. Hunter-Jones and J. Haferkamp, Ideal random quan- tum circuits pass the LXEB test, arXiv e-prints , arXiv:2602.22692 (2026), arXiv:2602.22692 [quant-ph]

work page arXiv 2026

Showing first 80 references.