  The development of quantum computing hardware is facing the challenge that
current-day quantum processors, comprising 50-100 qubits, already operate
outside the range of quantum simulation on classical computers. In this paper
we demonstrate that the simulation of classical limits can be a potent
diagnostic tool potentially mitigating this problem. As a testbed for our
approach we consider the transmon qubit processor, a computing platform in
which the coupling of large numbers of nonlinear quantum oscillators may
trigger destabilizing chaotic resonances. We find that classical and quantum
simulations lead to similar stability metrics (classical Lyapunov exponents vs.
quantum wave function participation ratios) in systems with $\mathcal{O}(10)$
transmons. However, the big advantage of classical simulation is that it can be
pushed to large systems comprising up to thousands of qubits. We exhibit the
utility of this classical toolbox by simulating all current IBM transmon chips,
including the recently announced 433-qubit processor of the Osprey generation,
as well as future devices with 1,121 qubits (Condor generation). For realistic
system parameters, we find a systematic increase of Lyapunov exponents with
system size, suggesting that larger layouts require added efforts in
information protection.
