Evaluating analytic gradients of quantum circuits by parameter shift rules, Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran, 2019Physical Review A, Vol. 99 (American Physical Society)DOI: 10.1103/PhysRevA.99.032331 - This academic paper introduces and formalizes the parameter-shift rule for computing exact gradients of quantum circuits, a standard technique in variational quantum algorithms.
Variational quantum algorithms, M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Hanamichi Yamasaki, and Patrick J. Coles, 2021Nature Reviews Physics, Vol. 3DOI: 10.1038/s42254-021-00348-9 - A comprehensive review of variational quantum algorithms, including an overview of optimization techniques and gradient calculation methods relevant to their training.
Gradients and optimization, PennyLane Documentation Team, 2024 (Xanadu) - Official documentation explaining how gradients, including the parameter-shift rule, are implemented and used within the PennyLane quantum machine learning framework.