System-environment Interaction Research Articles

Implications of non-Markovian quantum dynamics for the Landauer bound

We study the dynamics of a spin-1/2 particle interacting with a multi-spin environment, modelling the corresponding open system dynamics through a collision-based model. The environmental particles are prepared in individual thermal states, and we investigate the effects of a distribution of temperatures across the spin environment on the evolution of the system, particularly how thermalisation in the long-time limit is affected. We study the phenomenology of the heat exchange between system and environment and consider the information-to-energy conversion process, induced by the system–environment interaction and embodied by the Landauer principle. Furthermore, by considering an interacting-particles environment, we tune the dynamics of the system from an explicit Markovian evolution up to a strongly non-Markovian one, investigating the connections between non-Markovianity, the establishment of system–environment correlations, and the breakdown of the validity of Landauer principle.

Determining stationary-state quantum properties directly from system-environment interactions

Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona-fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady-state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering process.

Quantum correlations dynamics and decoherence of a three-qubit system subject to classical environmental noise

We address the dynamics of decoherence and quantum correlations (entanglement and discord) in a model of three non-interacting qubits, initially prepared in a maximally entangled pure Greenberger-Horne-Zeilinger (GHZ) state and then subjected to classical environmental noise in common, different and mixed environments. The noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and colored environmental noise. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the kind of the noise considered. On the one hand, our results clearly show that unlike what was found in the case of the two-qubit model analogous to the one here investigated, quantum correlations are not totally destroyed when the qubits are coupled to the noise in a common environment. On the other hand, the presence or absence of peculiar phenomena, such as entanglement, revivals and sudden death are observed. Furthermore, we show that the partial preservation of entanglement can be successfully detected by means of the suitable entanglement witness. Finally, in the case of static noise we find that the decoherence becomes stronger as the disorder of the environment increases whereas, for colored noise, it becomes stronger as the number of fluctuators increases.

Quantum chemistry and charge transport in biomolecules with superconducting circuits.

We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.

Approximate reversibility in the context of entropy gain, information gain, and complete positivity

There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics. Our first result is a remainder term for the entropy gain of a quantum channel. This result implies that a small increase in entropy under the action of a subunital channel is a witness to the fact that the channel's adjoint can be used as a recovery map to undo the action of the original channel. We apply this result to pure-loss, quantum-limited amplifier, and phase-insensitive quantum Gaussian channels, showing how a quantum-limited amplifier can serve as a recovery from a pure-loss channel and vice versa. Our second result regards the information gain of a quantum measurement, both without and with quantum side information. We find here that a small information gain implies that it is possible to undo the action of the original measurement if it is efficient. The result also has operational ramifications for the information-theoretic tasks known as measurement compression without and with quantum side information. Our third result shows that the loss of Holevo information caused by the action of a noisy channel on an input ensemble of quantum states is small if and only if the noise can be approximately corrected on average. We finally establish that the reduced dynamics of a system-environment interaction are approximately completely positive and trace preserving if and only if the data processing inequality holds approximately.

Time-local Heisenberg-Langevin equations and the driven qubit

The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg--Langevin equation. Extension to the driven qubit fails---except for weak excitation---due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.

Non-Markovian dynamics in ultracold Rydberg aggregates

We propose a setup of an open quantum system in which the environment can be tuned such that either Markovian or non-Markovian system dynamics can be achieved. The implementation uses ultracold Rydberg atoms, relying on their strong long-range interactions. Our suggestion extends the features available for quantum simulators of molecular systems employing Rydberg aggregates and presents a new test bench for fundamental studies of the classification of system–environment interactions and the resulting system dynamics in open quantum systems.

Coarse-Grained Theory of Biological Charge Transfer with Spatially and Temporally Correlated Noise.

System-environment interactions are essential in determining charge-transfer (CT) rates and mechanisms. We developed a computationally accessible method, suitable to simulate CT in flexible molecules (i.e., DNA) with hundreds of sites, where the system-environment interactions are explicitly treated with numerical noise modeling of time-dependent site energies and couplings. The properties of the noise are tunable, providing us a flexible tool to investigate the detailed effects of correlated thermal fluctuations on CT mechanisms. The noise is parametrizable by molecular simulation and quantum calculation results of specific molecular systems, giving us better molecular resolution in simulating the system-environment interactions than sampling fluctuations from generic spectral density functions. The spatially correlated thermal fluctuations among different sites are naturally built-in in our method but are not readily incorporated using approximate spectral densities. Our method has quantitative accuracy in systems with small redox potential differences (<kbT) and provides qualitative insights into systems with wide redox potential differences (≫kbT). Specifically, we find that the temporal correlations of site energies are critical in determining the coherent-incoherent transition, while the role of spatial correlations depends on the nature of the systems. In a system with repeated bridge units of the same chemistry, spatially correlated fluctuations enhance the charge delocalization and charge-transfer rates; however, in a system of units with different site energies, spatial correlations slow the fluctuations to bring units into degeneracy, in turn, slowing the charge-transfer rates. The spatial and temporal correlations of condensed phase medium fluctuations provide another source to control and tune the kinetics and dynamics of charge-transfer systems.

Sensing in the presence of an observed environment

Sensing in the presence of environmental noise is a problem of increasing practical interest. In a master equation description, where the state of the environment is unobserved, the effect of signal and noise is described by system operators only. In this context it is well-known that noise that is orthogonal on an external signal can be corrected for without perturbing the signal, while similarly efficient strategies for non-orthogonal signal and noise operators are not known. Here we make use of the fact that system-environment interaction typically arises via local two-body interactions describing the exchange of quanta between system and environment, which are observable in principle. That two-body-interactions are usually orthogonal on system operators, allows us to develop error corrected sensing supported by the observation of the quanta that are emitted into the environment. We describe such schemes and outline a realistic proof-of-principle experiment in an ion trap set-up.

Efficient simulation of non-Markovian system-environment interaction

In this work, we combine an established method for open quantum systems—the time evolving density matrix using orthogonal polynomials algorithm—with the transfer tensors formalism, a new tool for the analysis, compression and propagation of non-Markovian processes. A compact propagator is generated out of sample trajectories covering the correlation time of the bath. This enables the investigation of previously inaccessible long-time dynamics with linear effort, such as those ensuing from low temperature regimes with arbitrary, possibly highly structured, spectral densities. We briefly introduce both methods, followed by a benchmark to prove viability and combination synergies. Subsequently we illustrate the capabilities of this approach at the hand of specific examples and conclude our analysis by highlighting possible further applications of our method.

Hebbian Network of Self-Organizing Receptive Field Neurons as Associative Incremental Learner

Associative learning plays a major role in the formation of the internal dynamic engine of an adaptive system or a cognitive robot. Interaction with the environment can provide a sparse and discrete set of sample correlations of input–output incidences. These incidences of associative data points can provide useful hints for capturing underlying mechanisms that govern the system’s behavioral dynamics. In many approaches to solving this problem, of learning system’s input–output relation, a set of previously prepared data points need to be presented to the learning mechanism, as a training data, before a useful estimations can be obtained. Besides data-coding is usually based on symbolic or nonimplicit representation schemes. In this paper, we propose an incremental learning mechanism that can bootstrap from a state of complete ignorance of any representative sample associations. Besides, the proposed system provides a novel mechanism for data representation in nonlinear manner through the fusion of self-organizing maps and Gaussian receptive fields. Our architecture is based solely on cortically-inspired techniques of coding and learning as: Hebbian plasticity and adaptive populations of neural circuitry for stimuli representation. We define a neural network that captures the problem’s data space components using emergent arrangement of receptive field neurons that self-organize incrementally in response to sparse experiences of system–environment interactions. These learned components are correlated using a process of Hebbian plasticity that relates major components of input space to those of the output space. The viability of the proposed mechanism is demonstrated through multiple experimental setups from real-world regression and robotic arm sensory-motor learning problems.

Simulating Bosonic Baths with Error Bars.

We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths, the truncation of both the number of modes and the local Hilbert-space dimensions is necessary. We derive superexponential Lieb-Robinson-type bounds on the error when restricting the bath to finitely many modes and show how the error introduced by truncating the local Hilbert spaces may be efficiently monitored numerically. In this way we give error bounds for approximating the infinite system by a finite-dimensional one. As a consequence, numerical simulations such as the time-evolving density with orthogonal polynomials algorithm (TEDOPA) now allow for the fully certified treatment of the system-environment interaction.

Decoherence control by quantum decoherence itself.

We propose a general approach of protecting a two-level system against decoherence via quantum engineering of non-classical multiple superpositions of coherent states in a non-Markovian reservoir. The scheme surprisingly only uses the system-environment interaction responsible for the decoherence and projective measurements of the two-level system. We demonstrate the method on the example of an excitonic qubit in self-assembled semiconductor quantum dots coupled to the super-Ohmic reservoir of acoustic phonons.

Quantum Simulation of Dissipative Processes without Reservoir Engineering.

We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.

Probabilistically valid stochastic extensions of deterministic models for systems with uncertainty

Models capable of capturing and reproducing the variability observed in experimental trials can be valuable for planning and control in the presence of uncertainty. This paper reports on a new data-driven methodology that extends deterministic models to a stochastic regime and offers probabilistic guarantees of model fidelity. From an acceptable deterministic model, a stochastic one is generated, capable of capturing and reproducing uncertain system–environment interactions at given levels of fidelity. The reported approach combines methodological elements from probabilistic model validation and randomized algorithms, to simultaneously quantify the fidelity of a model and tune the distribution of random parameters in the corresponding stochastic extension, in order to reproduce the variability observed experimentally in the physical process of interest. The approach can be applied to an array of physical processes, the models of which may come in different forms, including differential equations; we demonstrate this point by considering examples from the areas of miniature legged robots and aerial vehicles.

Protecting theSWAPoperation from general and residual errors by continuous dynamical decoupling

We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both amplitude damping and dephasing errors. The other features the amplitude damping as a residual error and protects the qubits from dephasing errors only. In both settings, we investigate the interaction of qubits with common and independent environments separately. We study how errors affect the entanglement and fidelity for different environmental spectral densities.

Fluctuations of work in nearly adiabatically driven open quantum systems.

We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.

Analytical descriptions of cross-polarisation dynamics: relaxing the secular approximations

In this work, analytical expressions of the cross-polarisation (CP) dynamics under both static and magic-angle spinning (MAS) conditions are obtained by solving the generalised Liouville-von Neumann quantum mechanical equation beyond the standard approximations, i.e., reintroducing neglected non-secular terms in the system superoperator. Although the simple model of a two-spin system interacting with a spin bath gives a rather crude description of CP dynamics, it accounts well for the orientation dependence of CP in a static sample of ferrocene powder and permits to detect slight departures from the Hartmann–Hahn matching condition. This approach also has the advantage of yielding manageable analytical expressions that can be used even by less inclined or experienced workers to obtain results that are good enough in an operational sense. Moreover, the resulting spin diffusion rate constants containing different sources of anisotropy of the system–environment interaction as well as their dependence on the MAS frequency are related semi-quantitatively to the local network of dipolar interactions. Finally, it is shown that non-secular solutions improve significantly the analysis of CPMAS-based separated-local-field spectroscopy experimental data in the absence of homonuclear decoupling.

Dynamic Bayesian Networks for Fault Detection, Identification, and Recovery in Autonomous Spacecraft

This paper describes how to exploit the modeling features and inference capabilities of dynamic Bayesian networks (DBN), in designing and implementing an innovative approach to fault detection, identification, and recovery (FDIR) for autonomous spacecrafts (e.g., a Mars rover). In particular, issues like partial observability, uncertain system evolution and system-environment interaction, as well as the prediction and mitigation of imminent failures can be naturally addressed by the proposed approach. The DBN framework can augment the modeling and analytical power of standard FDIR methodologies, while still being able to be integrated into the usual system modeling procedures (like, for instance, fault tree analysis). An FDIR cycle composed of the tasks of diagnosis (identification of the current state of the system), prognosis (identification of the future state under the current conditions), and recovery (selection of the best set of actions the autonomous system can perform, in order to avoid critical situations) is introduced and characterized through a DBN model. In particular, by considering the execution of recovery actions in response to either a current or a future abnormal situation, both reactive as well as preventive recovery can be addressed respectively. The proposed approach has been implemented in an on-board software architecture called Anomaly resolution and prognostic health management for autonomy (ARPHA), realized during the Verifim study funded by the European Space Agency and jointly performed with Thales/Alenia Italy. We report on some of the results obtained by performing a case study concerning the FDIR analysis of the power supply system of the ExoMars rover, by considering different anomalous and failure simulated scenarios; we conclude that ARPHA is able to properly detect and deal with the simulated problems.

Influence of the External Environment Behaviour on the Banking System Stability

There are plenty of researches dedicated to financial system stability, which takes significant place in prevention of financial crisis and its consequences. However banking system and external environment interaction and customers behaviour influence on the banking system stability are poorly studied. Current paper propose agent-based model of banking system and its external environment. We show how customers behaviour characteristics affect a banking system stability. Optimal interval for total environmental funds towards banking system wealthy is performed.