  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.

Quantum Physics