  Recently, Lloyd and Montangero have made a brief research proposal on
universal quantum computation in integrable systems. The main idea is to encode
qubits into quantum action variables and build up quantum gates by the method
of resonant control. We study this proposal to argue quantum computation using
action variables as fault-tolerant quantum computation, whose fault-tolerance
is guaranteed by the quantum KAM theorem. Besides, we view the Birkhoff norm
form as a mathematical framework of the extended harmonic oscillator quantum
computation.
