Parameter-Shift Rules for Gradients in Boson Sampling Experiments
arXiv:2607.15160
The paper derives n‑th order parameter‑shift rules for computing gradients of Fock boson‑sampling probabilities in lossy interferometers, shows that such rules generally cannot be extended to Gaussian boson sampling except under specific matrix factorisations, and validates the approach on real hardware against finite‑difference methods.
Abstract
Using a robust photon loss model for photonic quantum experiments, we derive th order parameter-shift rules for computing gradients of Fock boson sampling transition probabilities where photons are sent into a lossy interferometer. We also show that in general it is not possible to generalize this gradient recipe to the case of Gaussian boson sampling. Only in the specific case where the transmission matrix of the interferometer can be factorized as a diagonal loss matrix premultiplied by a pure unitary it is possible to obtain parameter-shift rules with a finite order given by twice the total number of photons detected. We demonstrate the efficacy of the proposed method by comparing its performance against finite differences on real hardware.