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Featuring memory of past inputs is a fundamental requirement for machine learning models processing time-dependent data. In quantum reservoir computing, all architectures proposed so far rely on Markovian dynamics, which, as we prove,…

We study the dynamics of a dressed qubit implemented by a spinless fermion hopping between two lattice sites with each site strongly coupled to a bath of phonons. We employ Lang-Firsov transformation to make the problem tractable…

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time dependent oscillation of the…

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to…

We assess non-Markovianity of a quantum open-system dynamics through the violation of temporal bell-like inequalities in a controllable Nuclear Magnetic Resonance system. We investigate experimentally the connections between the violation…

We introduce a concept of non-coherent evolution of macroscopic quantum systems. We show that for weakly interacting systems such evolution is a Markovian stochastic process. The transition rates between system states, which characterize…

In this paper, we report findings of non-stationary behavior observed in a fully connected qubit network, utilizing a random unitary evolution model in open quantum system theory. The environmental effect is reflected in the partial swap…

Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information…

The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic potential, is studied focussing on its non-Markovian regime. Both an analytic approach and a stochastic wave function approach are used to…

The non-Markovia dynamics of quantum evolution plays an important role in open quantum sytem. However, how to quantify non-Markovian behavior and what can be obtained from non- Markovianity are still open questions, especially in complex…

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…

Realistic quantum mechanical systems are always exposed to an external environment. The presence of the environment often gives rise to a Markovian process in which the system loses information to its surroundings. However, many quantum…

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…

Using a recently proposed measure for divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a driven spin-$S$ system weakly coupled to a bosonic bath. The complete tomographic knowledge about the…

The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We…

The sine-Gordon equation exhibits a gap in its linear spectrum. That gives rise to memory, or non-Markovian, effects in the soliton formation processes. The generalized variational approach is suggested to derive the model equation that…

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the…

We propose a method for the dynamical control in three-level open systems and realize it in the experiment with a superconducting qutrit. Our work demonstrates that in the Markovian environment for a relatively long time (3 us), the…

Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…

In this paper, we study both open-loop control and closed-loop measurement feedback control of non-Markovian quantum dynamics arising from the interaction between a quantum system and its environment. We use the widely studied cavity…