  We propose to use the continuous version of the quantum Zeno effect to
eliminate leakage to higher energy states in superconducting quantum computing
architectures based on Josephson phase and flux qubits. We are particularly
interested in the application of this approach to the single-step
Greenberger-Horne-Zeilinger (GHZ) state protocol described in [A. Galiautdinov
and J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)]. While being
conceptually appealing, the protocol was found to be plagued with a number of
spectral crowding and leakage problems. Here we argue that by coupling the
qubits to a measuring device which continuously monitors leakage to higher
energy states (say, to a very lossy resonator of frequency omega =
E3(qubit)-E1(qubit), with 1 labeling the ground state of the qubit), we could
potentially restrict the multi-qubit system's evolution to its computational
subspace, thus circumventing the above mentioned problems.
