  We study decoherence induced by stochastic squeezing control errors
considering the particular implementation of Hadamard gate on optical and ion
trap holonomic quantum computers. We analytically obtain both the purity of the
final state and the fidelity for Hadamard gate when the control noise is
modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and
the fidelity oscillations depending on the choice of the initial superimposed
state. We derive a linear formulae connecting the gate fidelity and the purity
of the final state.
