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.
Physical Review A: Atomic, Molecular and Optical Physics

Kattemölle, J., & van Wezel, J. (2019). Dynamical fidelity susceptibility of decoherence-free subspaces. Physical Review A: Atomic, Molecular and Optical Physics, 99(6), 062340:1–062340:8. doi:10.1103/PhysRevA.99.062340