Exact treatment of quantum dynamics with coherent noise in complex many-body systems

In the NISQ era, noise plagues the possibility of useful quantum computation and in many-body systems, is a path to thermalization. Yet, its theoretical treatment has typically relied on approximate or numerical methods. Leveraging rotationally invariant random-matrix Hamiltonians, we develop calculational tools that produce exact analytic results for quantum dynamics under coherent noise. Focusing on the Gaussian Unitary Ensemble as the paradigmatic example without symmetries, we show how ensemble averages of Heisenberg evolutions yield families of noisy quantum channels. We can calculate exact expressions for any cumulant, going beyond traditional open-system techniques. Our results reveal unexpected phenomenology: the fidelity is nonmonotonic in the noise strength and never reaches the Haar limit - features that we connect to the structure of the underlying Lie group, as well as the behaviour of the spectral form factor. This framework extends to dynamics with symmetries by incorporating other RMT ensembles, revealing families of novel quantum channels as well as insights for thermalization and error correction.