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Efficient classical computation of the neural tangent kernel of quantum neural networks
Anderson Melchor Hernandez, Davide Pastorello, Giacomo De Palma
https://arxiv.org/abs/2508.04498

Efficient classical computation of the neural tangent kernel of quantum neural networks
We propose an efficient classical algorithm to estimate the Neural Tangent Kernel (NTK) associated with a broad class of quantum neural networks. These networks consist of arbitrary unitary operators belonging to the Clifford group interleaved with parametric gates given by the time evolution generated by an arbitrary Hamiltonian belonging to the Pauli group. The proposed algorithm leverages a key insight: the average over the distribution of initialization parameters in the NTK definition can …

Foundations of photonic quantum computation
Martin Bombardelli, G\'erard Fleury, Philippe Lacomme, Bogdan Vulpescu
https://arxiv.org/abs/2509.04266 https://

Foundations of photonic quantum computation
This work aims to introduce the fundamental concepts required to perform computations on photonic quantum computers by presenting the gates specific to this architecture and highlighting the connections between standard Pauli gates and those available in photonic systems. The introduction navigates between physical considerations related to the optical components used, theoretical aspects concerning quantum operators, and a more applied section introducing implementations using the Perceval lib…

A Verified Compiler for Quantum Simulation
Liyi Li, Fenfen An, Federico Zahariev, Zhi Xiang Chong, Amr Sabry, Mark Gordon
https://arxiv.org/abs/2509.18583 https://

Minimization of an Energy Functional for an Electron in the quantized Radiation Field over quasifree States
Matthias Herdzik
https://arxiv.org/abs/2507.17767 https://

Minimization of an Energy Functional for an Electron in the quantized Radiation Field over quasifree States
Building upon the works of Bach, Breteaux, and Tzaneteas (2013) and of Bach and Hach (2022), the Bogolubov-Hartree-Fock (BHF) energy of the Pauli-Fierz Hamiltonian is investigated. Upper and lower bounds on the BHF energy are derived, which suggest positivity of the minimizer, see Theorem IV.6. Under the assumption that the minimizer is indeed positive, a necessary condition on the minimizer is determined by introducing a parameterization, which simplifies the functions of operators appearing i…