  We present a benchmarking protocol for universal quantum computers, achieved
through the simulation of random dynamical quantum maps. This protocol provides
a holistic assessment of system-wide error rates, encapsulating both gate
inaccuracies and the errors associated with mid-circuit qubit measurements and
resets. By employing random quantum circuits and segmenting mid-circuit qubit
measurement and reset in a repeated fashion, we steer the system of qubits to
an ensemble of steady-states. These steady-states are described by random
Wishart matrices, and align with the steady-state characteristics previously
identified in random Lindbladian dynamics, including the universality property.
The protocol assesses the resulting ensemble probability distribution measured
in the computational basis, effectively avoiding a tomographic reconstruction.
Our various numerical simulations demonstrate the relationship between the
final distribution and different error sources. Additionally, we implement the
protocol on state-of-the-art transmon qubits provided by IBM Quantum, drawing
comparisons between empirical results, theoretical expectations, and
simulations derived from a fitted noise model of the device.
