  Quantum control is necessary for a variety of modern quantum technologies as
it allows to optimally manipulate quantum systems. An important problem in
quantum control is to establish whether the control objective functional has
trapping behaviour or no, namely if it has or no traps -- controls from which
it is difficult to escape by local search optimization methods. Higher order
traps were previously introduced in [A. N. Pechen, D. J. Tannor, "Are there
traps in quantum control landscapes?", Phys. Rev. Lett., 106 (2011), 120402],
where 3-rd order traps were found. In this note we show that traps of
arbitrarily high order exist for controllable quantum systems with special
symmetry in the Hamiltonian.
