  The efficient probing of spectral features of quantum many-body systems is
important for characterising and understanding the structure and dynamics of
quantum materials. In this work, we establish a framework for probing the
excitation spectrum of quantum many-body systems with quantum simulators. Our
approach effectively realises a spectral detector by processing the dynamics of
observables with time intervals drawn from a defined probability distribution,
which only requires native time evolution governed by the Hamiltonian without
any ancilla. The critical element of our method is the engineered emergence of
frequency resonance such that the excitation spectrum can be probed. We show
that the time complexity for transition energy estimation has a logarithmic
dependence on simulation accuracy, and discuss the noise e robustness of our
spectroscopic method. We present simulation results for the spectral features
of typical quantum systems, including quantum spins, fermions and bosons. We
experimentally demonstrate how spectroscopic features of spin lattice models
can be probed with IBM quantum devices.
