We introduce an approach to characterize the dynamics of disordered quantum networks. Each quantum element (i.e., each node) of the network experiences the other nodes as an effective environment that can be self-consistently represented by a Feynman-Vernon influence functional. For networks having the topology of locally treelike graphs, these Feynman-Vernon (FV) functionals can be determined by a new version of the cavity or belief propagation (BP) method. Here, we find the fixed point solution of this version of BP for a network of uniform quantum harmonic oscillators. Then, we estimate the effects of the disorder in these networks within the replica symmetry ansatz. We show that over a large time interval, at small disorder, the real part of the FV functional induces decoherence and classicality while at sufficiently large disorder the Feynman-Vernon functional tends to zero and the coherence survives, signaling in a time setting, the onset of an Anderson's transition.
We introduce an approach to characterize the dynamics of disordered quantum networks. Each quantum element (i.e., each node) of the network experiences the other nodes as an effective environment that can be self-consistently represented by a Feynman-Vernon influence functional. For networks having the topology of locally treelike graphs, these Feynman-Vernon (FV) functionals can be determined by a new version of the cavity or belief propagation (BP) method. Here, we find the fixed point solution of this version of BP for a network of uniform quantum harmonic oscillators. Then, we estimate the effects of the disorder in these networks within the replica symmetry ansatz. We show that over a large time interval, at small disorder, the real part of the FV functional induces decoherence and classicality while at sufficiently large disorder the Feynman-Vernon functional tends to zero and the coherence survives, signaling in a time setting, the onset of an Anderson's transition.
quantum system interacting with other quantum systems experiences these other systems asan effective environment. The environment is the result of integrating out all the other degrees of freedom in the network, and can be represented by a Feynman-Vernon influence functional (IF)acting on system of interest. A network is characterized by the constitutive systems, how they interact, and the topology of those interactions. Here we show that for networks having the topology of locally tree-like graphs, the Feynman-Vernon influence functional can be determined in a new version of the cavity or Belief Propagation (BP) method. In the BP update stage, cavity IFs are mapped to cavity IFs, while in the BP output stage cavity IFs are combined to output IFs. We compute the fixed point of of this version of BP for harmonic oscillator systems interacting uniformly. We discuss Replica Symmetry and the effects of disorder in this context.
Systems with quenched disorder host fascinating dynamical phases including many-body localization. Theoretical description of such phases proves challenging since it requires disorder-averaging over many configurations, and very rare configurations may have an important effect. Here, the authors introduce a new method, based on the Feynman-Vernon influence functional, that allows one to directly access the disorder-averaged dynamics of quantum spin chains. This formulation provides a starting point for describing the many-body localization transition using variational and analytical techniques.
The effect of an electron heat bath on the motion of an electron system is studied using a quantum Langevin equation and deriving the influence functional of the Feynman-Vernon approach. The generating functional for the time-dependent, finite-temperature correlation functions of a disordered electron system with interactions is written down, and some of its symmetry properties are analyzed. Since the disorder only affects the time evolution of the system our formalism avoids the replica trick and provides a natural physical framework for studying a large variety of open problems in the field of disordered systems. As an example, we give an explicit expression for the averaged generating functional for a disordered electron system in the presence of a Coulomb interaction in terms of two complex matrix fields.
In this paper, we develop a blended dynamics framework for open quantum networks with diffusive couplings. The network consists of qubits interconnected through Hamiltonian couplings, environmental dissipation, and consensus-like diffusive interactions. Such networks commonly arise in spontaneous emission processes and non-Hermitian quantum computing, and their evolution follows a Lindblad master equation. Blended dynamics theory is well established in the classical setting as a tool for analyzing emergent behaviors in heterogeneous networks with diffusive couplings. Its key insight is to blend the local dynamics rather than the trajectories of individual nodes. Perturbation analysis then shows that, under sufficiently strong coupling, all node trajectories tend to stay close to those of the blended system over time. We first show that this theory extends naturally to the reduced-state dynamics of quantum networks, revealing classical-like clustering phenomena in which qubits converge to a shared equilibrium or a common trajectory determined by the quantum blended reduced-state dynamics. We then extend the analysis to qubit coherent states using quantum Laplacians and induced graphs, proving orbit attraction of the network density operator toward the quantum blended coherent dynamics, establishing the emergence of intrinsically quantum and dynamically clustering behaviors. Finally, numerical examples validate the theoretical results.
The title of the present dissertation Decoherence in Quantum Network sounds very general and all-inclusive. Indeed it embraces two topics (decoherence and quantum network) from the area of Quantum Mechanics each of which is described in all respects by a huge literature developed in the last three decades [...]. Quantum decoherence, as the name lets it mean, is the mechanism that makes a quantum system loose its coherence properties, and with them the capability of giving rise to interference phenomena or to other interesting quantum effects [...]. The key idea promoted by decoherence is the insight that realistic quantum systems are never isolated, but are immersed in the surrounding environment and interact continuously with it [...]. As an example one may consider a two-level quantum system (i.e. a quantum bit, usually shortened with a terminology from information science to \\qubit" ) in contact with a wide environment. Hence, quantum systems are open systems, and continuously interact or exchange information with an external environment whose degrees of freedom are too numerous to be monitored. The resulting correlation between the system and the environment spoils quantum coherence and brings about the transition from a pure quantum state to a mixture of quantum state resulting a classical state. To describe decoherence different kind of approaches can be used (for example Master equation, random matrix, etc). A quantum network typically consists of a number of quantum objects (e.g., atoms, ions, quantum dots, cavities, etc.), to be referred to hereafter as the sites or the nodes of the network. They can interact and the interactions (or their correlations) will be usually described by the edges of a graph. Quantum networks can address different information processing tasks. For instance a quantum state can be transferred from qubit to qubit down a chain solely due to the interactions, that is according to the laws of quantum physics [...]. Quantum networks offer us new opportunities and phenomena as compared to classical networks. An extension to large scale of the idea of a quantum network could lead to a futurible quantum internet [...]. The study of networks has traditionally been the territory of graph theory [...], also with the advent of their quantum versions. Within simple quantum network model information processing is usually described by assuming perfect control of the underlying graph. However, this is not much realistic since randomness is often present and it leads to decoherence effects [...]. In contrast, the conservation of coherence is essential for any quantum information process [...], hence there is a persistent interest in decoherence effects in quantum networks, which motivate us to study models for describing such noisy effects. We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
Recent experimental and theoretical works have made much progress toward understanding nonequilibrium phenomena in thermalizing systems, which act as thermal baths for their small subsystems, and many-body localized systems, which fail to do so.The description of time evolution in many-body systems is generally challenging due to the dynamical generation of quantum entanglement.In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional.Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics.The central object in our approach is the influence matrix, which describes the effect of the system on the dynamics of a local subsystem.For translationally invariant models, we formulate a self-consistency equation for the influence matrix.For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD).Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin.For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works.In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time.In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the influence matrix temporal entanglement is low.A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective "statistical-mechanics" description.We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes.The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods and to further characterizing quantum ergodicity or lack thereof.