  In idealized models of a quantum register and its environment, quantum
information can be stored indefinitely by encoding it into a decoherence-free
subspace (DFS). Nevertheless, perturbations to the idealized
register-environment coupling will cause decoherence in any realistic setting.
Expanding a measure for state preservation, the dynamical fidelity, in powers
of the strength of the perturbations, we prove stability to linear order is a
generic property of quantum state evolution. The effect of noise perturbation
is quantified by a concise expression for the strength of the quadratic,
leading order, which we define as the dynamical fidelity susceptibility of
DFSs. Under the physical restriction that noise acts on the register
$k$-locally, this susceptibility is bounded from above by a polynomial in the
system size. These general results are illustrated by two physically relevant
examples. Knowledge of the susceptibility can be used to increase coherence
times of future quantum computers.
