  Within quantum information, many methods have been proposed to avoid or
correct the deleterious effects of the environment on a system of interest. In
this work, expanding on our earlier paper [G. A. Paz-Silva et al., Phys. Rev.
Lett. 108, 080501 (2012), arXiv:1104.5507], we evaluate the applicability of
the quantum Zeno effect as one such method. Using the algebraic structure of
stabilizer quantum error correction codes as a unifying framework, two
open-loop protocols are described which involve frequent non-projective (i.e.,
weak) measurement of either the full stabilizer group or a minimal generating
set thereof. The effectiveness of the protocols is measured by the distance
between the final state under the protocol and the final state of an idealized
evolution in which system and environment do not interact. Rigorous bounds on
this metric are derived which demonstrate that, under certain assumptions, a
Zeno effect may be realized with arbitrarily weak measurements, and that this
effect can protect an arbitrary, unknown encoded state against the environment
arbitrarily well.
