Reliable processing of quantum information is crucial for quantum technologies development. Characterizing the ubiquitous out-of-equilibrium quantum systems [1-3] is essential for designing optimal control and quantum sensing strategies. However, this task is highly challenging due to the complex high-order correlations and non-stationary nature. In this talk, I will present methods to characterize the decoherence of out-of-equilibrium quantum systems [1,4-6]. Using quantum simulations with Solid-State Nuclear Magnetic Resonance, we quantify "out-of-time order correlations" (OTOCs [2-3]) to define a critical threshold in disturbances to achieve reliable control of large quantum systems [1,4-5]. Furthermore, we develop a framework for quantum sensing the dynamics of out-of-equilibrium systems . The sensor manifests spectral and non-Markovian properties, providing a quantum technology to probe time-correlation properties and mitigate the decoherence effects of non-stationary environments.
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