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Quantum algorithms for simulating quantum systems provide a clear andprovable advantage over classical algorithms in fault-tolerant settings. Thereis also interest in quantum algorithms and the experiments that implement thesealgorithms for NISQ settings. In these settings, various sources of noise anderror need to be accounted for when executing any experiments. Recently, NISQdevices have been verified as versatile testbeds for open quantum systems. Ithas been demonstrated that NISQ devices can simulate simple quantum channels.Our goal is to apply NISQ devices to the more complicated problem of simulatingconvex mixtures of quantum channels. We consider two specific cases; convexmixtures of Markovian channels that result in a non-Markovian channel (M+M=nM)and convex mixtures of non-Markovian channels that result in a Markovianchannel (nM+nM=M). For our first case, we consider convex mixtures ofNon-Markovian depolarising channels. For our second case, we consider convexmixtures of Markovian Pauli channels. We show that efficient circuits, thataccount for the topology of currently available devices and current levels ofdecoherence, can be constructed by avoiding traditional approaches such asStinespring Dilation etc. We also present a strategy for the implementation ofa process tomography that yields a CPTP channel.

Digital Simulation of Convex Mixtures of Markovian and Non-Markovian Single Qubit Channels on NISQ Devices