Abel S Criado JC Spannowsky M Training neural networks with universal adiabatic quantum computing Front Artif Intell 2024 7 1368569 10.3389/frai.2024.1368569
Abel S, Criado J.C., Spannowsky M (2022) Completely quantum neural networks. Phys Rev A 106:022601. https://doi.org/10.1103/PhysRevA.106.022601
Anschuetz ER, Kiani BT (2022) Quantum variational algorithms are swamped with traps. Nat Commun 13(1):7760. https://doi.org/10.1038/s41467-022-35364-5
Ban Y Chen X Torrontegui E Solano E Casanova J Speeding up quantum perceptron via shortcuts to adiabaticity Sci Rep 2021 11 1 5783 10.1038/s41598-021-85208-3
Benedetti M Lloyd E Sack S Fiorentini M Parameterized quantum circuits as machine learning models Quant Sci Technol 2019 4 4 043001 10.1088/2058-9565/ab4eb5
Biamonte J Wittek P Pancotti N Rebentrost P Wiebe N Lloyd S Quantum machine learning Nature 2017 549 7671 195 202 10.1038/nature23474
Bittel L, Kliesch M (2021) Training variational quantum algorithms is np-hard. Phys Rev Lett 127:120502. https://doi.org/10.1103/PhysRevLett.127.120502
Braunstein SL, Loock P (2005) Quantum information with continuous variables. Rev Mod Phys 77:513–577. https://doi.org/10.1103/RevModPhys.77.513
Cerezo M, Arrasmith A, Babbush R, Benjamin SC, Endo S, Fujii K, McClean JR, Mitarai K, Yuan X, Cincio L, Coles PJ (2021) Variational quantum algorithms. Nat Rev Phys 3(9):625–644. https://doi.org/10.1038/s42254-021-00348-9
Chatterjee R, Yu T (2016) Generalized coherent states, reproducing kernels, and quantum support vector machines. arXiv:1612.03713. https://doi.org/10.26421/qic17.15-16
Cindrak S Donvil B Lüdge K Jaurigue L Enhancing the performance of quantum reservoir computing and solving the time-complexity problem by artificial memory restriction Phys Rev Res 2024 6 013051 10.1103/PhysRevResearch.6.013051
Cowan G (1998) Statistical Data Analysis. Oxford University Press, Oxford. See Ch. 10 for the Poisson-to-Gaussian limit and central-limit reasoning
Das S Siopsis G Weedbrook C Continuous-variable quantum gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices Phys Rev A 2018 97 022315 10.1103/PhysRevA.97.022315
Dunjko V, Taylor JM, Briegel HJ (2016) Quantum-enhanced machine learning. Phys Rev Lett 117:130501. https://doi.org/10.1103/PhysRevLett.117.130501
Farhi E, Goldstone J, Gutmann S (2014) A quantum approximate optimization algorithm. arXiv:1411.4028. https://doi.org/10.48550/arXiv.1411.4028
Fuentes J Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields Sci Rep 2020 10 1 22256 10.1038/s41598-020-79309-8
Fujii K Nakajima K Harnessing disordered-ensemble quantum dynamics for machine learning Phys Rev Appl 2017 8 024030 10.1103/PhysRevApplied.8.024030
Havlíček V, Córcoles AD, Temme K, Harrow AW, Kandala A, Chow JM, Gambetta JM (2019) Supervised learning with quantum-enhanced feature spaces. Nature 567(7747):209–212. https://doi.org/10.1038/s41586-019-0980-2
Huang H-Y, Kueng R, Preskill J (2021) Information-theoretic bounds on quantum advantage in machine learning. Phys Rev Lett 126:190505. https://doi.org/10.1103/PhysRevLett.126.190505
Killoran N, Bromley TR, Arrazola JM, Schuld M, Quesada N, Lloyd S (2019) Continuous-variable quantum neural networks. Phys Rev Res 1:033063. https://doi.org/10.1103/PhysRevResearch.1.033063
Kornjača M, Hu H-Y, Zhao C, Wurtz J, Weinberg P, Hamdan M, Zhdanov A, Cantu SH, Zhou H, Bravo RA, Bagnall K, Basham JI, Campo J, Choukri A, DeAngelo R, Frederick P, Haines D, Hammett J, Hsu N, Hu M-G, Huber F, Jepsen PN, Jia N, Karolyshyn T, Kwon M, Long J, Lopatin J, Lukin A, Macrì T, Marković O, Martínez-Martínez LA, Meng X, Ostroumov E, Paquette D, Robinson J, Rodriguez PS, Singh A, Sinha N, Thoreen H, Wan N, Waxman-Lenz D, Wong T, Wu K-H, Lopes PLS, Boger Y, Gemelke N, Kitagawa T, Keesling A, Gao X, Bylinskii A, Yelin SF, Liu F, Wang S-T (2024) Large-scale quantum reservoir learning with an analog quantum computer. arXiv:2407.02553. https://doi.org/10.48550/arXiv.2407.02553
Langer CE (2006) High fidelity quantum information processing with trapped ions. PhD thesis, University of Colorado. PhD thesis. See Sec. 2.4 for Poisson photon-count statistics in fluorescence detection
Lau H-K Pooser R Siopsis G Weedbrook C Quantum machine learning over infinite dimensions Phys Rev Lett 2017 118 080501 3678579 10.1103/PhysRevLett.118.080501
McClean JR Romero J, Babbush R, Aspuru-Guzik A: The theory of variational hybrid quantum-classical algorithms New J Phys 2016 18 2 023023 10.1088/1367-2630/18/2/023023
McClean JR Boixo S Smelyanskiy VN Babbush R Neven H Barren plateaus in quantum neural network training landscapes Nat Commun 2018 9 1 4812 10.1038/s41467-018-07090-4
Mielnik B (1986) Evolution loops. J Math Phys 27(9):2290–2306. https://doi.org/10.1063/1.527001. https://pubs.aip.org/aip/jmp/article-pdf/27/9/2290/19254253/2290_1_online.pdf
Mielnik B Quantum operations: technical or fundamental challenge? J Phys A: Math Theor 2013 46 38 385301 3105604 10.1088/1751-8113/46/38/385301
Mielnik B Quantum control: discovered, repeated and reformulated ideas mark the progress J Phys: Conf Ser 2014 512 1 012035 10.1088/1742-6596/512/1/012035
Mielnik B Ramírez A Ion traps: some semiclassical observations Phys Scr 2010 82 5 055002 10.1088/0031-8949/82/05/055002
Mielnik B Ramírez A Magnetic operations: a little fuzzy mechanics? Phys Scr 2011 84 4 045008 10.1088/0031-8949/84/04/045008
Mielnik B, Fuentes J (2024) Conceptual problems in quantum squeezing. In: Kielanowski P, Beltita D, Dobrogowska A, Goliński T (eds) Geometric Methods in Physics XL, pp 413–426. Springer, Cham. https://doi.org/10.1007/978-3-031-62407-0_28
Mitarai K, Negoro M, Kitagawa M, Fujii K (2018) Quantum circuit learning. Phys Rev A 98:032309. https://doi.org/10.1103/PhysRevA.98.032309
Mockus J Application of Bayesian approach to numerical methods of global and stochastic optimization J Global Optim 1994 4 4 347 365 1275752 10.1007/BF01099263
Mujal P, Martínez-Peña R, Giorgi GL, Soriano MC, Zambrini R (2023) Time-series quantum reservoir computing with weak and projective measurements. npj Quant Inf 9(1):16 (2023). https://doi.org/10.1038/s41534-023-00682-z
Mujal P, Martínez-Peña R, Nokkala J, García-Beni J, Giorgi GL, Soriano MC, Zambrini R (2021) Opportunities in quantum reservoir computing and extreme learning machines. Adv Quant Technol 4(8):2100027. https://doi.org/10.1002/qute.202100027. https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/qute.202100027
Ortiz Marrero C, Kieferová M, Wiebe N (2021) Entanglement-induced barren plateaus. PRX Quant 2:040316. https://doi.org/10.1103/PRXQuantum.2.040316
Paul W (1990) Electromagnetic traps for charged and neutral particles. Rev Mod Phys 62:531–540. https://doi.org/10.1103/RevModPhys.62.531
Peruzzo A, McClean J, Shadbolt P, Yung M-H, Zhou X-Q, Love PJ, Aspuru-Guzik A, O’Brien JL (2014) A variational eigenvalue solver on a photonic quantum processor. Nat Commun 5(1):4213. https://doi.org/10.1038/ncomms5213
Rebentrost P Mohseni M Lloyd S Quantum support vector machine for big data classification Phys Rev Lett 2014 113 130503 10.1103/PhysRevLett.113.130503
Rifkin R Klautau A In defense of one-vs-all classification J Mach Learn Res 2004 5 101 141 2247975
Schuld M, Killoran N (2021) Quantum machine learning in feature Hilbert spaces. Phys Rev Lett 122:040504. https://doi.org/10.1103/PhysRevLett.122.040504
Schuld M, Petruccione F (2018) Supervised learning with quantum computers, 1st edn. Quant Sci Technol. Springer. https://doi.org/10.1007/978-3-319-96424-9. Springer Nature Switzerland AG 2018
Shen K, Jobst B, Shishenina E, Pollmann F (2024) Classification of the fashion-mnist dataset on a quantum computer. arXiv:2403.02405. https://doi.org/10.48550/arXiv.2403.02405
Torrontegui E, García-Ripoll JJ (2019) Unitary quantum perceptron as efficient universal approximator(a). Europhys Lett 125(3):30004. https://doi.org/10.1209/0295-5075/125/30004
Verdon G, Broughton M, Biamonte J (2019) A quantum algorithm to train neural networks using low-depth circuits. arXiv:1712.05304. https://doi.org/10.48550/arXiv.1712.05304
Xiao T, Zhai X, Wu X, Fan J, Zeng G (2023) Practical advantage of quantum machine learning in ghost imaging. Commun Phys 6:171. https://doi.org/10.1038/s42005-023-01290-1
Xu H Xiao T Huang J He M Fan J Zeng G Toward heisenberg limit without critical slowing down via quantum reinforcement learning Phys Rev Lett 2025 134 12 120803 10.1103/PhysRevLett.134.120803