Seminar on "Parameter Shift Rule With the Optimal Phase Selection" by Dr. Liubov Markovich

30-th April at 11.00, Moscow time, ACTP will hold a seminar "Parameter Shift Rule With the Optimal Phase Selection" by Dr. Liubov Markovich (Leiden University, aQa).
Abstract
Parameter shift rules enable the estimation of the derivatives of expectation values with respect to the dynamical evolution of a state. Thus, they provide a valuable tool in variational optimization and insight into the dynamical behavior of quantum systems. Constructing parameter shift rules applicable to complex dynamical generators is useful towards improving the control of analog quantum simulation devices and extending the applicability of variational quantum simulating methods. However, parameter shift rules are typically designed only for dynamical generators with highly degenerate or equidistant eigenvalues, such as Pauli operators, commonplace in the construction of parameterized quantum circuits. For generators with irregularly-spaced eigenvalues, effective rules have not been established. We provide insights about the optimal design of a parameter shift rule tailored to various sorts of spectral information that may be available. The proposed method targets the calculation of any linear combination of k-th derivatives with respect to the conjugate variable of a generator with a known spectrum, regardless of how close the eigenvalues are to each other. We discuss the optimal choice of parameter shifts, minimizing their number and the variance of the target estimator. Furthermore, we discuss the construction of parameter shift rules when only partial information about the generator spectrum is known.