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Attend a 52-minute seminar exploring advanced parameter shift rules for quantum systems with irregular eigenvalue spectra. Learn how to estimate derivatives of expectation values in quantum dynamical evolution, moving beyond traditional methods limited to highly degenerate or equidistant eigenvalues like Pauli operators. Discover optimal design strategies for parameter shift rules that work with any known spectrum, regardless of eigenvalue spacing, and understand how to calculate linear combinations of k-th derivatives with respect to conjugate variables. Explore techniques for minimizing the number of parameter shifts while reducing variance in target estimators, and examine methods for constructing parameter shift rules when only partial spectral information is available. Gain insights into improving control of analog quantum simulation devices and extending variational quantum simulation methods through these advanced mathematical frameworks presented by Dr. Liubov Markovich from Leiden University.
