Commutation simulator for open quantum dynamics

Recent progress in quantum simulation and algorithms has demonstrated a rapid expansion in capabilities. The search continues for new techniques and applications to exploit quantum advantage. Here we propose an innovative method to investigate directly the properties of a time-dependent density operator ρ(t). Using generalised quantum commutation simulators, we can directly compute the expectation value of the commutation relation and thus of the rate of change of ρ(t). The approach can be utilized as a quantum eigen-vector solver for the von Neumann equation and a decoherence investigator for the Lindblad equation, by using just the statistics of single-qubit measurements. A simple but important example is demonstrated in three qubits.