This has in turn given rise to a proliferation of results on the characterisation of memory effects and non-Markovian dynamics. The increasing ability to coherently control an ever increasing number of individual quantum systems, together with the discovery of quantum coherence in complex biological systems, 6 has brought to light several scenarios in which the Markovian assumption fails. This consideration already illustrates how, despite its indubitable foundational nature, open quantum systems theory is still far from being completely understood and, in fact, it is peppered with unanswered questions of deep nature. 1, 2, 3, 4, 5 When these assumptions are not satisfied, e.g., for strong system–environment interaction and/or long-living environmental correlations, we enter the intricate (and somewhat fuzzy) reign of non-Markovian dynamics. Only under certain assumptions, known as the Born–Markov approximation, one can derive a general equation in the so called Lindblad form, able to describe the physical evolution of quantum states. Contrarily to the case of closed quantum systems, where the equation of motion describing the state dynamics is the Schrödinger equation, the general form of the master equation for an open quantum system is not known. Master equations are either phenomenologically postulated or derived microscopically from a Hamiltonian model of quantum system plus environment. Generally, the dynamics of open quantum systems are described in terms of a master equation, i.e., the equation of motion for the reduced density operator describing the quantum state of the system. For these reasons its range of applicability is extremely wide, from solid state physics to quantum field theory, from quantum chemistry and biology to quantum thermodynamics, from foundations of quantum theory to quantum technologies. 1, 2, 3 In its most general formulation, it allows us to describe the out-of-equilibrium properties of quantum systems, it provides a theoretical framework to assess the quantum measurement problem, and it gives us the tools to investigate, understand and counter the deleterious effects of noise on quantum technologies. The theory of open quantum systems studies the dynamics of quantum systems interacting with their surroundings. All these results are obtained using IBM Q Experience processors publicly available and remotely accessible online. Moreover, we realise proof-of-principle reservoir engineering for entangled state generation, demonstrate collisional models, and verify revivals of quantum channel capacity and extractable work, caused by memory effects. Indeed, we experimentally implement one and two-qubit open quantum systems, both unital and non-unital dynamics, Markovian and non-Markovian evolutions. Our main result is to prove the great versatility of the IBM Q Experience processors. Generally, each individual experiment demonstrates a specific open quantum system model, or at most a specific class. During the last decade an increasing number of experiments have successfully tackled the task of simulating open quantum systems in different platforms, from linear optics to trapped ions, from nuclear magnetic resonance (NMR) to cavity quantum electrodynamics. Here, we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum systems theory. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. The advent of noisy intermediate-scale quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics.
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