Author(s): Zhijian Lai, Jiang Hu, Dong An, and Zaiwen Wen Parameter-shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evaluate the cost function at different parameter shifts, then use specific coefficients to combine them linearly to obtain t… [Phys. Rev. Applied 25, 014005] Published Mon Jan 05, 2026