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Register a new userUnboxing Quantum Black Box Models: Learning Non-Markovian Dynamics
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Characterizing the memory properties of the environment has become critical for the high-fidelity control of qubits and other advanced quantum systems. However, current non-Markovian tomography techniques are either limited to discrete superoperators, or they employ machine learning methods, neither of which provide physical insight into the dynamics of the quantum system. To circumvent this limitation, we design learning architectures that explicitly encode physical constraints like the properties of completely-positive trace-preserving maps in a differential form. This method preserves the versatility of the machine learning approach without sacrificing the efficiency and fidelity of traditional parameter estimation methods. Our approach provides the physical interpretability that machine learning and opaque superoperators lack. Moreover, it is aware of the underlying continuous dynamics typically disregarded by superoperator-based tomography. This paradigm paves the way to noise-aware optimal quantum control and opens a path to exploiting the bath as a control and error mitigation resource.
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Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects. Here we develop a method to extract the information about the unknown environment from a series of projective single-shot measurements on the system (without resorting to the process tomography). The method is based on embedding the non-Markovian system dynamics into a Markovian dynamics of the system and the effective reservoir of finite dimension. The generator of Markovian embedding is learned by the maximum likelihood estimation. We verify the method by comparing its prediction with an exactly solvable non-Markovian dynamics. The developed algorithm to learn unknown quantum environments enables one to efficiently control and manipulate quantum systems.
We investigate the roles of different environmental models on quantum correlation dynamics of two-qubit composite system interacting with two independent environments. The most common environmental models (the single-Lorentzian model, the squared-Lorentzian model, the two-Lorentzian model and band-gap model) are analyzed. First, we note that for the weak coupling regime, the monotonous decay speed of the quantum correlation is mainly determined by the spectral density functions of these different environments. Then, by considering the strong coupling regime we find that, contrary to what is stated in the weak coupling regime, the dynamics of quantum correlation depends on the non-Markovianity of the environmental models, and is independent of the environmental spectrum density functions.
We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.
We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e. the open dynamics is modelled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ancillas, which are subsequently traced out. In this setting non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of memory depth where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a non-monotonic time behaviour of the heat flux serves as an indicator of non-Markovian behaviour.
We investigate the dynamics of quantum correlations (QC) under the effects of reservoir memory, as a resource for quantum information and computation tasks. Quantum correlations of two-qubit systems are used for implementing quantum teleportation successfully, and for investigating how teleportation fidelity, violation of Bell-CHSH inequality, quantum steering and entanglement are connected with each other under the influence of noisy environments. Both Markovian and non-Markovian channels are considered, and it is shown that the decay and revival of correlations follow the hierarchy of quantum correlations in the state space. Noise tolerance of quantum correlations are checked for different types of unital and non-unital quantum channels, with and without memory. The quantum speed limit time $(tau_{QSL})$ is investigated from the perspective of memory of quantum noise, and the corresponding dynamics is used to analyze the evolution of quantum correlations. We establish the connection between information backflow, quantum speed limit time and dynamics of quantum correlations for non-Markovian quantum channels.
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