Temporal defects in discrete-time quantum dynamics: stochastic unitary channels and the Lindblad limit

We study a class of discrete-time quantum dynamics in which the unitary update rule is subjectto rare, local failures. Each failure replaces the intended unitary evolution with an alternativeunitary operator drawn from a fixed set. The resulting evolution is described by a stochasticunitary channel, which is completely positive and trace-preserving (CPTP) by construction. In thelimit of small failure probability and continuous time, we derive the corresponding Lindblad masterequation. The derivation does not assume that the failure operators are close to identity or that theycommute with the Hamiltonian. We discuss the Markovian approximation, the scaling of memoryeffects, and the generality of the resulting dissipative structure. The framework provides a minimalmicroscopic motivation for open-system dynamics without invoking an external environment.