arxiv: 2605.10577 · v1 · submitted 2026-05-11 · 🪐 quant-ph

Recognition: no theorem link

Training continuously-coupled reconfigurable photonic chips with quantum machine learning

Denis Stanev , Nicol\`o Spagnolo , Fabio Sciarrino

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:31 UTC · model grok-4.3

classification 🪐 quant-ph

keywords reconfigurable photonic chipscontinuously-coupled waveguidesquantum machine learningblack-box optimizationunitary programmingsingle-photon measurementstwo-photon interferenceintegrated interferometers

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The pith

A black-box machine learning method programs continuously-coupled photonic chips to any target unitary using limited single- and two-photon measurements.

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

The paper shows that machine learning can configure reconfigurable interferometers built from continuously-coupled waveguide arrays even when traditional analytical recipes fail. It treats the entire chip as a black box and tunes its parameters by feeding in a modest number of single-photon and two-photon interference measurements. This avoids the need for precise knowledge of every internal coupling or phase value. The approach is verified through simulations on both planar and three-dimensional layouts. If the method holds, it removes a major obstacle to deploying diverse integrated photonic circuits for quantum information tasks.

Core claim

We devise a machine learning based approach for this task, using a black box methodology that does not rely on precise a-priori modeling of the circuit internal architectures. We verify the effectiveness and the robustness of this approach via numerical simulations on different continuously-coupled waveguides layouts, either with planar or 3D structures. The proposed method makes use of a limited number of single- and two-photon measurements, making it suitable for optical quantum information processing.

What carries the argument

The black-box machine learning optimizer that adjusts the chip's tunable parameters by minimizing the mismatch between observed single- and two-photon statistics and those expected for the target unitary.

If this is right

The method succeeds for both planar and three-dimensional continuously-coupled waveguide layouts.
Only a small number of single- and two-photon measurements are required to train the model.
No detailed internal circuit model is needed, allowing flexibility across different fabrication designs.
The trained configurations are suitable for optical quantum information processing tasks.
The approach extends the range of usable integrated interferometer architectures.

Where Pith is reading between the lines

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

Real fabricated chips with fabrication imperfections could still be calibrated if the measurement budget is increased modestly.
The same black-box training loop might be run in situ on the device to compensate for environmental drift.
Scaling the method to larger arrays would test whether measurement overhead grows linearly or sub-linearly with the number of waveguides.
The technique could be combined with other variational quantum algorithms that already use photonic hardware.

Load-bearing premise

Numerical simulations on idealized waveguide models accurately predict performance on real fabricated chips and the chosen measurements contain enough information to reach arbitrary target unitaries.

What would settle it

Apply the machine-learning-trained settings to a real continuously-coupled chip, perform the same single- and two-photon measurements, and check whether the achieved fidelity to the target unitary matches the simulation prediction within experimental error bars.

Figures

Figures reproduced from arXiv: 2605.10577 by Denis Stanev, Fabio Sciarrino, Nicol\`o Spagnolo.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗

read the original abstract

Integrated photonic technologies have recently shown significant advances, enabling the possibility to implement reconfigurable interferometers with increasing size. One of the main tasks to fully exploit the capabilities of reconfigurable integrated interferometers is the possibility to precisely program their operation to perform a desired target unitary. While recipes are known for circuit layouts based on a cascade of beam-splitter and phase-shifter operations, a methodology applicable for reconfigurable continuously-coupled waveguide arrays is currently missing. Here, we devise a machine learning based approach for this task, using a black box methodology that does not rely on precise a-priori modeling of the circuit internal architectures. We verify the effectiveness and the robustness of this approach via numerical simulations on different continuously-coupled waveguides layouts, either with planar or 3D structures. The proposed method makes use of a limited number of single- and two-photon measurements, making it suitable for optical quantum information processing. The obtained results open the perspective of employing this methodology as an effective tool to program the operation of integrated interferometers designed via different architectures.

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

A black-box ML calibration method for continuously-coupled photonic arrays that works in ideal simulations but leaves real-chip transfer untested.

read the letter

This paper shows a machine learning procedure to set continuously-coupled waveguide arrays to target unitaries using only single- and two-photon measurements, without building an explicit model of the internal couplings. The approach is new for these layouts, where standard cascaded recipes do not apply, and the authors demonstrate it numerically on both planar and 3D structures. That is the concrete advance: a general, measurement-driven optimizer that could in principle work across different chip designs. The simulations indicate that limited photon data can train the device in the perfect-model case, which is a reasonable starting point for the problem they set out to solve. The black-box framing is practical because it sidesteps the need for precise a-priori knowledge of fabrication parameters. The central weakness is that all verification stays inside idealized waveguide Hamiltonians. There are no injected fabrication errors, no propagation losses, no wavelength dependence, and no experimental data on actual chips. Because training and testing use the same perfect simulator, the results do not yet show whether the learned mapping survives the mismatches that real devices introduce. The abstract also gives little visibility into training hyperparameters, convergence behavior, or quantitative error metrics. This work is aimed at groups building or using reconfigurable photonic processors who need a calibration route for non-standard layouts. It is worth sending to peer review so that referees can examine the simulation details and ask for robustness checks against realistic imperfections. The idea addresses a genuine gap even if the current evidence is still preliminary.

Referee Report

2 major / 2 minor

Summary. The paper claims that a black-box machine-learning procedure can program continuously-coupled reconfigurable photonic waveguide arrays to realize arbitrary target unitaries, using only a limited number of single- and two-photon measurements and without requiring an internal model of the chip architecture. The approach is demonstrated exclusively through numerical simulations on idealized planar and 3D waveguide Hamiltonians.

Significance. If the central claim holds beyond idealized models, the method could simplify calibration of large-scale reconfigurable photonic interferometers for quantum information tasks by avoiding detailed device modeling. The use of limited photon statistics is a practical strength, but the absence of experimental validation or tests against fabrication variance limits immediate impact.

major comments (2)

[Numerical Simulations] Numerical Simulations section: all training and test data are generated from the same ideal waveguide Hamiltonian (both planar and 3D layouts). No simulations incorporate fabrication imperfections such as coupling-strength disorder, propagation losses, or wavelength dependence, which directly undermines the claim that the learned mapping will remain effective on real fabricated chips.
[Method] Method description (black-box optimization): the loss is defined solely against measurement data from the ideal simulator. Because the training distribution matches the test distribution exactly, the reported success rates do not address the transfer gap that the abstract positions as the key advantage over model-based recipes.

minor comments (2)

[Abstract] The abstract states that the method is 'robust,' yet the only robustness shown is to the choice of ML hyperparameters on perfect models; clarify what 'robustness' refers to in the results.
[Results] Figure captions and text should explicitly state the number of single- and two-photon measurements used per target unitary and the dimension of the unitaries tested.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will revise the paper to incorporate additional simulations that better demonstrate robustness under realistic conditions.

read point-by-point responses

Referee: [Numerical Simulations] Numerical Simulations section: all training and test data are generated from the same ideal waveguide Hamiltonian (both planar and 3D layouts). No simulations incorporate fabrication imperfections such as coupling-strength disorder, propagation losses, or wavelength dependence, which directly undermines the claim that the learned mapping will remain effective on real fabricated chips.

Authors: We agree that the current simulations use idealized Hamiltonians and do not yet incorporate fabrication imperfections. This limits the direct evidence for performance on real devices. In the revised manuscript we will add a new set of numerical experiments that include coupling-strength disorder, propagation losses, and wavelength dependence. These will be generated by perturbing the underlying Hamiltonian during both training and evaluation, allowing us to quantify how the black-box optimization maintains high-fidelity unitaries when the measurement data deviate from the ideal model. revision: yes
Referee: [Method] Method description (black-box optimization): the loss is defined solely against measurement data from the ideal simulator. Because the training distribution matches the test distribution exactly, the reported success rates do not address the transfer gap that the abstract positions as the key advantage over model-based recipes.

Authors: The black-box procedure is intended for direct use on physical hardware, where the loss is computed from actual single- and two-photon measurements on the fabricated chip and therefore automatically incorporates any deviations from the ideal model. In the presented simulations we deliberately employed an ideal Hamiltonian to isolate the performance of the optimization algorithm itself. To explicitly demonstrate the transfer advantage, the revised manuscript will include additional trials in which training is performed on a perturbed Hamiltonian (simulating fabrication variance) and the resulting control parameters are evaluated on the target unitary; the resulting fidelities will be compared against a model-based baseline that assumes perfect knowledge of the internal architecture. revision: yes

Circularity Check

0 steps flagged

No circularity: black-box ML training against external simulation data is self-contained

full rationale

The paper presents a machine-learning procedure that optimizes chip controls to match target unitaries using only single- and two-photon measurement statistics. This optimization is performed against data generated from an external idealized waveguide simulator; the training loop does not define its own loss or target in terms of the fitted parameters, nor does any cited result reduce to a self-citation chain. Verification on planar and 3D layouts remains an independent numerical benchmark rather than a tautological re-expression of the input model. No load-bearing step collapses by construction to the method's own assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach assumes standard waveguide propagation models in simulations and standard machine-learning optimization assumptions; no new physical axioms are introduced.

free parameters (1)

machine learning hyperparameters
Network architecture, learning rate, and training epochs are chosen to fit the simulation data.

axioms (1)

domain assumption Waveguide coupling and phase shifts can be modeled accurately enough in numerical simulations to represent real devices.
Invoked when claiming robustness from simulation results.

pith-pipeline@v0.9.0 · 5480 in / 1111 out tokens · 30670 ms · 2026-05-12T04:31:31.913623+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages · 4 internal anchors

[1]

Arute, K

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M. P. Harrigan, M. J. Hartmann, A. Ho, M. Hoffman, T. Huang, T. S....

work page 2019
[2]

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, 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 (2020)

work page 2020
[3]

Zhong, Y.-H

H.-S. Zhong, Y.-H. Deng, J. Qin, H. Wang, M.-C. Chen, L.-C. Peng, Y.-H. Luo, D. Wu, S.-Q. Gong, H. Su, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N.-L. Liu, J. J. Renema, C.-Y. Lu, and J.-W. Pan, Phase-programmable gaussian boson sampling using stimulated squeezed light, Phys. Rev. Lett.127, 180...

work page 2021
[4]

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, Y. 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. Zh...

work page 2021
[5]

L. S. Madsen, F. Laudenbach, M. Falamarzi.Askarani, F. Rortais, T. Vincent, J. F. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, A. E. Lita, T. Ger- rits, S. W. Nam, V. D. Vaidya, M. Menotti, I. Dhand, Z. Vernon, N. Quesada, and J. Lavoie, Quantum compu- tational advantage with a programmable photonic pro- cessor, Nature606, 75 (2022)

work page 2022
[6]

Deng, Y.-C

Y.-H. Deng, Y.-C. Gu, H.-L. Liu, S.-Q. Gong, H. Su, Z.- J. Zhang, H.-Y. Tang, M.-H. Jia, J.-M. Xu, M.-C. Chen, H.-S. Zhong, J. Qin, H. Wang, L.-C. Peng, J. Yan, Y. Hu, J. Huang, H. Li, Y. Li, Y. Chen, X. Jiang, L. Gan, 17 G. Yang, L. You, L. Li, N.-L. Liu, J. J. Renema, C.- Y. Lu, and J.-W. Pan, Gaussian boson sampling with pseudo-photon-number resolving ...

work page 2023
[7]

Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, Evidence for the utility of quantum computing before fault tolerance, Nature618, 500 (2023)

work page 2023
[8]

Acharya, D

R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buck- ley, D...

work page 2024
[9]

J. Wang, F. Sciarrino, A. Laing, and M. G. Thompson, Integrated photonic quantum technologies, Nat. Photon. 14, 273–284 (2019)

work page 2019
[10]

P. P. Rohde, Simple scheme for universal linear-optics quantum computing with constant experimental com- plexity using fiber loops, Phys. Rev. A91, 012306 (2015)

work page 2015
[11]

Bartlett, A

B. Bartlett, A. Dutt, and S. Fan, Deterministic photonic quantum computation in a synthetic time dimension, Op- tica8, 1515 (2021)

work page 2021
[12]

P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X.-M. Jin, M. Barbieri, W. S. Kolthammer, and I. A. Walmsley, Linear optical quantum computing in a single spatial mode, Phys. Rev. Lett.111, 150501 (2013)

work page 2013
[13]

Carosini, V

L. Carosini, V. Oddi, F. Giorgino, L. M. Hansen, B. Seron, S. Piacentini, T. Guggemos, I. Agresti, J. C. Loredo, and P. Walther, Programmable multiphoton quantum interference in a single spatial mode, Sci. Adv. 10, eadj0993 (2024)

work page 2024
[14]

Flamini, N

F. Flamini, N. Spagnolo, and F. Sciarrino, Photonic quantum information processing: a review, Rep. Prog. Phys.82, 016001 (2018)

work page 2018
[15]

Fukui and S

K. Fukui and S. Takeda, Building a large-scale quantum computer with continuous-variable optical technologies, J. Phys. B: At. Mol. Opt. Phys.55, 012001 (2022)

work page 2022
[16]

Gottesman, A

D. Gottesman, A. Kitaev, and J. Preskill, Encoding a qubit in an oscillator, Phys. Rev. A64, 012310 (2001)

work page 2001
[17]

Liu and H.-R

W.-Q. Liu and H.-R. Wei, Linear optical universal quan- tum gates with higher success probabilities, Adv. Quan- tum Technol.6, 2300009 (2023)

work page 2023
[18]

Bartolucci, P

S. Bartolucci, P. Birchall, H. Bomb´ ın, H. Cable, C. Daw- son, M. Gimeno-Segovia, E. Johnston, K. Kieling, N. Nickerson, M. Pant, F. Pastawski, T. Rudolph, and C. Sparrow, Fusion-based quantum computation, Nat. Commun.14, 912 (2023)

work page 2023
[19]

Y. Zhan, H. Zhang, R. Erbanni, A. Burger, L. Wan, X. Jiang, S. Chae, A. Liu, D. Poletti, and L. C. Kwek, Loop quantum photonic chip for coherent multi-time- step evolution (2024), arXiv:2411.11307 [quant-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[20]

Paesani, Y

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, Generation and sampling of quantum states of light in a silicon chip, Nat. Phys.15, 925–929 (2019)

work page 2019
[21]

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Experimental realization of any discrete unitary opera- tor, Phys. Rev. Lett.73, 58 (1994)

work page 1994
[22]

W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walmsley, Optimal design for uni- versal multiport interferometers, Optica3, 1460 (2016)

work page 2016
[23]

Giordani, F

T. Giordani, F. Hoch, G. Carvacho, N. Spagnolo, and F. Sciarrino, Integrated photonics in quantum technolo- gies, Riv. Nuovo Cim.46, 71 (2023)

work page 2023
[24]

Peruzzo, M

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. W¨ orhoff, Y. Bromberg, Y. Silberberg, M. G. Thomp- son, and J. L. O’Brien, Quantum walks of correlated pho- tons, Science329, 1500 (2010). 18

work page 2010
[25]

F. Hoch, S. Piacentini, T. Giordani, Z.-N. Tian, M. Iu- liano, C. Esposito, A. Camillini, G. Carvacho, F. Cecca- relli, N. Spagnolo, A. Crespi, F. Sciarrino, and R. Osel- lame, Reconfigurable continuously-coupled 3d photonic circuit for boson sampling experiments, npj Quantum Inf.8, 35 (2022)

work page 2022
[26]

Y. Yang, R. J. Chapman, B. Haylock, F. Lenzini, Y. N. Joglekar, M. Lobino, and A. Peruzzo, Programmable high-dimensional hamiltonian in a photonic waveguide array, Nat. Commun.15, 50 (2024)

work page 2024
[27]

Y. Yang, R. J. Chapman, A. Youssry, B. Haylock, F. Lenzini, M. Lobino, and A. Peruzzo, Programmable quantum circuits in a large-scale photonic waveguide ar- ray, npj Quantum Inf.11, 19 (2025)

work page 2025
[28]

Zhou, X.-W

W.-H. Zhou, X.-W. Wang, R.-J. Ren, Y.-X. Fu, Y.-J. Chang, X.-Y. Xu, H. Tang, and X.-M. Jin, Multi-particle quantum walks on 3d integrated photonic chip, Light: Sci. Appl.13, 296 (2024)

work page 2024
[29]

Z.-Q. Jiao, J. Gao, W.-H. Zhou, X.-W. Wang, R.-J. Ren, X.-Y. Xu, L.-F. Qiao, Y. Wang, and X.-M. Jin, Two- dimensional quantum walks of correlated photons, Optica 8, 1129 (2021)

work page 2021
[30]

Poulios, R

K. Poulios, R. Keil, D. Fry, J. D. A. Meinecke, J. C. F. Matthews, A. Politi, M. Lobino, M. Gr¨ afe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, Quantum walks of correlated photon pairs in two-dimensional waveguide arrays, Phys. Rev. Lett.112, 143604 (2014)

work page 2014
[31]

D. N. Biggerstaff, R. Heilmann, A. A. Zecevik, M. Gr¨ afe, M. A. Broome, A. Fedrizzi, S. Nolte, A. Szameit, A. G. White, and I. Kassal, Enhancing coherent transport in a photonic network using controllable decoherence, Nat. Commun.7, 11282 (2016)

work page 2016
[32]

Caruso, A

F. Caruso, A. Crespi, A. G. Ciriolo, F. Sciarrino, and R. Osellame, Fast escape of a quantum walker from an in- tegrated photonic maze, Nat. Commun.7, 11682 (2016)

work page 2016
[33]

Albertsson, P

K. Albertsson, P. Altoe, D. Anderson, M. Andrews, J. P. Araque Espinosa, A. Aurisano, L. Basara, A. Bevan, W. Bhimji, D. Bonacorsi, P. Calafiura, M. Campanelli, L. Capps, F. Carminati, S. Carrazza, T. Childers, E. Co- niavitis, K. Cranmer, C. David, D. Davis, J. Duarte, M. Erdmann, J. Eschle, A. Farbin, M. Feickert, N. F. Castro, C. Fitzpatrick, M. Floris...

work page 2018
[34]

Litjens, T

G. Litjens, T. Kooi, B. E. Bejnordi, A. A. A. Setio, F. Ciompi, M. Ghafoorian, J. A. van der Laak, B. van Ginneken, and C. I. S´ anchez, A survey on deep learning in medical image analysis, Med. Image Anal.42, 60–88 (2017)

work page 2017
[35]

Vaswani, N

A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, Attention is all you need, inAdvances in Neural Infor- mation Processing Systems, Vol. 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vish- wanathan, and R. Garnett (Curran Associates, Inc., 2017)

work page 2017
[36]

DeepSeek-AI: X. Bi, D. Chen, G. Chen, S. Chen, D. Dai, C. Deng, H. Ding, K. Dong, Q. Du, Z. Fu, H. Gao, K. Gao, W. Gao, R. Ge, K. Guan, D. Guo, J. Guo, G. Hao, Z. Hao, Y. He, W. Hu, P. Huang, E. Li, G. Li, J. Li, Y. Li, Y. K. Li, W. Liang, F. Lin, A. X. Liu, B. Liu, W. Liu, X. Liu, X. Liu, Y. Liu, H. Lu, S. Lu, F. Luo, S. Ma, X. Nie, T. Pei, Y. Piao, J. Q...

work page internal anchor Pith review Pith/arXiv arXiv 2024
[37]

A. I. Khan and S. Al-Habsi, Machine learning in com- puter vision, Procedia Comput. Sci.167, 1444 (2020)

work page 2020
[38]

Stanev, N

D. Stanev, N. Spagnolo, and F. Sciarrino, Deterministic optimal quantum cloning via a quantum-optical neural network, Phys. Rev. Res.5, 013139 (2023)

work page 2023
[39]

G. R. Steinbrecher, J. P. Olson, D. Englund, and J. Car- olan, Quantum optical neural networks, npj Quantum Inf.5, 60 (2019)

work page 2019
[40]

Zhang and Q

Y. Zhang and Q. Ni, Recent advances in quantum ma- chine learning, Quantum Eng.2, e34 (2020)

work page 2020
[41]

Bordoni, D

S. Bordoni, D. Stanev, T. Santantonio, and S. Gi- agu, Long-lived particles anomaly detection with parametrized quantum circuits, Particles6, 297–311 (2023)

work page 2023
[42]

Bartlett and S

B. Bartlett and S. Fan, Universal programmable photonic architecture for quantum information processing, Phys. Rev. A101, 042319 (2020)

work page 2020
[43]

Suprano, D

A. Suprano, D. Zia, L. Innocenti, S. Lorenzo, V. Ci- mini, T. Giordani, I. Palmisano, E. Polino, N. Spagnolo, F. Sciarrino, G. M. Palma, A. Ferraro, and M. Pater- nostro, Photonic quantum extreme learning machine, in Quantum 2.0 Conference and Exhibition(Optica Pub- lishing Group, 2024) p. QW4A.2

work page 2024
[44]

F. Hoch, E. Caruccio, G. Rodari, T. Francalanci, A. Suprano, T. Giordani, G. Carvacho, N. Spagnolo, S. Koudia, M. Proietti, C. Liorni, F. Cerocchi, R. Albiero, N. Di Giano, M. Gardina, F. Ceccarelli, G. Corrielli, U. Chabaud, R. Osellame, M. Dispenza, and F. Sciarrino, Quantum machine learning with adaptive boson sam- pling via post-selection, Nat. Commun...

work page 2025
[45]

K. H. Nielsen, Y. Wang, E. Deacon, P. I. Sund, Z. Liu, S. Scholz, A. D. Wieck, A. Ludwig, L. Mi- dolo, A. S. Sørensen, S. Paesani, and P. Lodahl, Pro- grammable nonlinear quantum photonic circuits (2024), arXiv:2405.17941 [quant-ph]. 19

work page arXiv 2024
[46]

H. Tang, L. Banchi, T.-Y. Wang, X.-W. Shang, X. Tan, W.-H. Zhou, Z. Feng, A. Pal, H. Li, C.-Q. Hu, M. S. Kim, and X.-M. Jin, Generating haar-uniform randomness us- ing stochastic quantum walks on a photonic chip, Phys. Rev. Lett.128, 050503 (2022)

work page 2022
[47]

Whitfield, C

J. Whitfield, C. A. Rodriguez-Rosario, and Aspuru-Guzi, Quantum stochastic walks: A generalization of classi- cal random walks and quantum walks, Phys. Rev. A81, 022323 (2010)

work page 2010
[48]

QuTiP 5: The Quantum Toolbox in Python

N. Lambert, E. Gigu` ere, P. Menczel, B. Li, P. Hopf, G. Su´ arez, M. Gali, J. Lishman, R. Gadhvi, R. Agar- wal, A. Galicia, N. Shammah, P. Nation, J. R. Johans- son, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, Qutip 5: The quantum toolbox in python (2024), arXiv:2412.04705 [quant-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[49]

Heurtel, A

N. Heurtel, A. Fyrillas, G. d. Gliniasty, R. Le Bihan, S. Malherbe, M. Pailhas, E. Bertasi, B. Bourdoncle, P.- E. Emeriau, R. Mezher, L. Music, N. Belabas, B. Valiron, P. Senellart, S. Mansfield, and J. Senellart, Perceval: A Software Platform for Discrete Variable Photonic Quan- tum Computing, Quantum7, 931 (2023)

work page 2023
[50]

Robbins and S

H. Robbins and S. Monro, A stochastic approximation method, Ann. Math. Stat.22, 400–407 (1951)

work page 1951
[51]

Kiefer and J

J. Kiefer and J. Wolfowitz, Stochastic estimation of the maximum of a regression function, Ann. Math. Stat.23, 462–466 (1952)

work page 1952
[52]

Amari, Backpropagation and stochastic gradient de- scent method, Neurocomputing5, 185–196 (1993)

S.-i. Amari, Backpropagation and stochastic gradient de- scent method, Neurocomputing5, 185–196 (1993)

work page 1993
[53]

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
[54]

Tillmann, C

M. Tillmann, C. Schmidt, and P. Walther, On unitary reconstruction of linear optical networks, J. Opt.18, 114002 (2016)

work page 2016
[55]

Spagnolo, E

N. Spagnolo, E. Maiorino, C. Vitelli, M. Bentivegna, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, Learning an unknown transformation via a genetic ap- proach, Sci. Rep.7, 14316 (2017)

work page 2017
[56]

F. Hoch, T. Giordani, N. Spagnolo, A. Crespi, R. Osel- lame, and F. Sciarrino, Characterization of multimode linear optical networks, Adv. Photonics Nexus2, 016007 (2023)

work page 2023
[57]

Abbas, R

A. Abbas, R. King, H.-Y. Huang, W. J. Huggins, R. Movassagh, D. Gilboa, and J. R. McClean, On quan- tum backpropagation, information reuse, and cheating measurement collapse (2023), arXiv:2305.13362 [quant- ph]

work page arXiv 2023
[58]

Chau and M

M. Chau and M. C. Fu, An overview of stochastic approx- imation, inHandbook of Simulation Optimization, edited by M. C. Fu (Springer New York, New York, NY, 2015) pp. 149–178

work page 2015
[59]

Lewis, R

D. Lewis, R. Wiersema, J. Carrasquilla, and S. Bose, Geodesic algorithm for unitary gate design with time-independent hamiltonians (2025), arXiv:2401.05973 [quant-ph]

work page arXiv 2025
[60]

C. Lee, H. Hasegawa, and S. Gao, Complex-valued neu- ral networks: A comprehensive survey, IEEE/CAA J. Autom. Sin.9, 1406 (2022)

work page 2022
[61]

Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)

D.-A. Clevert, T. Unterthiner, and S. Hochreiter, Fast and accurate deep network learning by exponential linear units (elus) (2016), arXiv:1511.07289 [cs.LG]

work page Pith review arXiv 2016
[62]

D. P. Kingma and J. Ba, Adam: A method for stochastic optimization (2017), arXiv:1412.6980 [cs.LG]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[63]

Srivastava, G

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, Dropout: a simple way to prevent neural networks from overfitting, J. Mach. Learn. Res. 15, 1929–1958 (2014)

work page 1929
[64]

S. L. Smith, P.-J. Kindermans, C. Ying, and Q. V. Le, Don’t decay the learning rate, increase the batch size (2017), arXiv:1711.00489 [cs.LG]

work page arXiv 2017