The experimental benchmarking of quantum computers and simulators is a formidable task. In fact, many of the existing benchmarking methods cannot be applied to the several-dozens qubit processors available today. By monitoring the purity loss in a given devices it is possible to quantify the effect of the environment in the computation or simulation and separate incoherent from coherent errors. Unfortunately, present methods for evaluating purity are either non-scalable or limited to short range correlations. We present methods for evaluating the change in purity during quantum evolution due to coupling to a Markovian environment. We use a variant of this method for measuring the entanglement buildup in quantum circuits and another variant for measuring changes in state overlap. These methods are scalable as they involve only a few observables which are relatively easy to measure in the devices available today. Finally, we use similar techniques for mitigating Markovian noise. Preliminary experimental results from one of IBM’s quantum computers will be presented.