  Solid state devices for quantum bit computation (qubits) are not perfect
isolated two-level systems, since additional higher energy levels always exist.
One example is the Josephson flux qubit, which consists on a mesoscopic SQUID
loop with three Josephson junctions operated at or near a magnetic flux of half
quantum. We study intrinsic leakage effects, i.e., direct transitions from the
allowed qubit states to higher excited states of the system during the
application of pulses for quantum computation operations. The system is started
in the ground state and rf- magnetic field pulses are applied at the qubit
resonant frequency with pulse intensity $f_p$. A perturbative calculation of
the average leakage for small $f_p$ is performed for this case, obtaining that
the leakage is quadratic in $f_p$, and that it depends mainly on the matrix
elements of the supercurrent. Numerical simulations of the time dependent
Schr\"odinger equation corresponding to the full Hamiltonian of this device
were also performed. From the simulations we obtain the value of $f_p$ above
which the two-level approximation breaks down, and we estimate the maximum Rabi
frequency that can be achieved. We study the leakage as a function of the ratio
$\alpha$ among the Josephson energies of the junctions of the device, obtaining
the best value for minimum leakage ($\alpha\approx0.85$). The effects of flux
noise on the leakage are also discussed.
