  We show that the three-junction SQUID device designed for the Josephson flux
qubit can be used to study the dynamics of quantum chaos when operated at high
energies. We determine the parameter region where the system is classically
chaotic. We calculate numerically the fidelity or Loschmidt echo (LE) in the
quantum dynamics under perturbations in the magnetic field and in the critical
currents, and study different regimes of the LE. We discuss how the LE could be
observed experimentally considering both the preparation of the initial state
and the measurement procedure.
