  An extension to the quantum Langevin equation is derived, that is valid in
the incoherent hopping regime, and which allows one to incorporate quantum
tunneling events. This is achieved by the inclusion of additional stochastic
variables in the Langevin equation representing the tunneling events. A
systematic derivation of this extension and of its regime of validity is
presented. The study is motivated by efforts to determine the error in reading
the state of a super-conducting quantum bit.
