  A major problem in exploiting microscopic systems for developing a new
technology based on the principles of Quantum Information is the influence of
noise which tends to work against the quantum features of such systems. It
becomes then crucial to understand how noise affects the evolution of quantum
circuits: several techniques have been proposed among which stochastic
differential equations (SDEs) can represent a very convenient tool. We show how
SDEs naturally map any Markovian noise into a linear operator, which we will
call a noise gate, acting on the wave function describing the state of the
circuit, and we will discuss some examples. We shall see that these gates can
be manipulated like any standard quantum gate, thus simplifying in certain
circumstances the task of computing the overall effect of the noise at each
stage of the protocol. This approach yields equivalent results to those derived
from the Lindblad equation; yet, as we show, it represents a handy and fast
tool for performing computations, and moreover, it allows for fast numerical
simulations and generalizations to non Markovian noise. In detail we review the
depolarizing channel and the generalized amplitude damping channel in terms of
this noise gate formalism and show how these techniques can be applied to any
quantum circuit.
