  We discuss monitoring the time evolution of an analog quantum simulator via a
quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND
variable of interest is the `energy' of the quantum many-body system,
represented by the Hamiltonian of the quantum simulator. We describe a physical
implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in
tweezer arrays using laser dressing schemes for a broad class of spin models.
As an application, we discuss a quantum protocol for measuring the spectral
form factor of quantum many-body systems, where the aim is to identify
signatures of ergodic vs. non-ergodic dynamics, which we illustrate for
disordered 1D Heisenberg and Floquet spin models on Rydberg platforms. Our
results also provide the physical ingredients for running quantum phase
estimation protocols for measurement of energies, and preparation of energy
eigenstates for a specified spectral resolution on an analog quantum simulator.
