Kraus decomposition for chaotic environments including time-dependent subsystem Hamiltonians

We derive an exact and explicit Kraus decomposition for the reduced density of a quantum system simultaneously interacting with time-dependent external fields and a chaotic environment of thermodynamic dimension. We test the accuracy of the Kraus decomposition against exact numerical results for a CNOT gate performed on two qubits of an (N+2) qubit statically flawed isolated quantum computer. Here the N idle qubits comprise the finite environment. We obtain very good agreement even for small N.