  We experimentally assess the suitability of transmon qubits with fixed
frequencies and fixed interactions for the realization of analogue quantum
simulations of spin systems. We test a set of necessary criteria for this goal
on a commercial quantum processor using full quantum process tomography and
more efficient Hamiltonian tomography. Significant single qubit errors at low
amplitudes are identified as a limiting factor preventing the realization of
analogue simulations on currently available devices. We additionally find
spurious dynamics in the absence of drive pulses, which we identify with
coherent coupling between the qubit and a low dimensional environment. With
moderate improvements, analogue simulation of a rich family of time-dependent
many-body spin Hamiltonians may be possible.
