  Dynamical correlations reveal important out-of-equilibrium properties of the
underlying quantum many-body system, yet they are notoriously difficult to
measure in experiments. While measurement protocols for dynamical correlations
based on Hadamard tests for qubit quantum devices exist, they do not
straightforwardly extend to qudits. Here, we propose a modified protocol to
overcome this limitation by decomposing qudit observables into unitary
operations that can be implemented and probed in a quantum circuit. We
benchmark our algorithm numerically at the example of quench dynamics in a
spin-1 XXZ chain with finite shot noise and demonstrate advantages in terms of
signal-to-noise ratio over established protocols based on linear response. Our
scheme can readily be implemented on various platforms and offers a wide range
of applications like variational quantum optimization or probing thermalization
in many-body systems.
