We investigate the dynamics of the quantum weightless neuron (qRAM) regarding entanglement. Previous works used a quantum extractor operator (QEO) to iterate the qRAM. With the QEO the qRAM output channel can be fed back or iterated despite possible entanglement of the overall output quantum state. Two measures are used here for the quantitative analysis: von Neummann entropy and entanglement entropy. We find that entanglement is disturbed and even increased when the QEO is used. In contrast entanglement stays unchanged under coherent feedback. The results indicate that QEO produces a more diverse dynamics and can be viewed as an environment interaction operator but not with decaying properties. A descriptive analyse of the entropy and entanglement dynamics is presented.
We investigate the dynamics of the quantum weightless neuron (qRAM) regarding entanglement. Previous works used a quantum extractor operator (QEO) to iterate the qRAM. With the QEO the qRAM output channel can be fed back or iterated despite possible entanglement of the overall output quantum state. Two measures are used here for the quantitative analysis: von Neummann entropy and entanglement entropy. We find that entanglement is disturbed and even increased when the QEO is used. In contrast entanglement stays unchanged under coherent feedback. The results indicate that QEO produces a more diverse dynamics and can be viewed as an environment interaction operator but not with decaying properties. A descriptive analyse of the entropy and entanglement dynamics is presented.
A wide spectrum of social, biological, physical, chemical and computational systems have been investigated by the tools and techniques from the field of Dynamical Systems Theory to formalize the behaviour in time and quantify and qualify the parametric variations of those systems. In Biology in particular, studies have shown that learning neuron maximization can occur in specific dynamics conditions where information processing is optimized. This it may be expected that some of those conditions can be recognized and used in artificial models. This work studies the quantum artificial neuron weightless qRAM behavior, from the design iteration models - taking into account the physical and mathematical conditions of quantum computing that restricts the extraction of information at every time step - to its parametric analysis where converging behaviors, damped or oscillatory, are detailed. Tools of dynamical systems like orbits diagram and time series qualitatively illustrate its temporal variability. The main contribution of this work is to detail the neuron qRAM behavior so that the results can be used within the machine learning area, coupled with larger systems to achieve maximum learning tasks. As result, we propose a novel dynamical neuron model, named Quadratic Extraction Model (QEM), we perfom parametric studies of the existing models where underdamped, overdamped and undamped behaviour are encountered, and we present apresentation of a neuron configuration inside a quantum architecture with chaos behaviour. A quantitative measure model to compare dynamics orbits was also proposed.
A parametric analysis of a quantum neuron node dynamics is proposed using an output qubit extraction protocol employed in previous works. The proposed classification method is composed of 5 different types of dynamics which explain the parameter changing behavior. The initial conditions analysis for each dynamics type is investigated. This parametric analysis gives a better understanding of the dynamics suggesting how fine-tune the system parameters can influence the system expected behaviour allowing e.g. For applications in patten recognition and information retrieval.
A model of discrete dynamics of entanglement of a bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied by an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of subsystems. For some mixed states having different marginal entropies of the subsystems we find an asymmetry in speed of entanglement decay. The entanglement of these states decreases faster, if the depolarizing channel acts on the ``classical'' subsystem, characterized by smaller marginal entropy.
The advent of noisy intermediate-scale quantum (NISQ) devices has not only opened up new possibilities to studying quantum computational benefits, but it has also presented new challenges associated with noise and short coherence times. Entanglement is one of the inherent resources that can be used to perform quantum computation and implement the performance and reliability of quantum algorithms. This paper looks at entanglement dynamics in NISQ machines subjected to natural noises. The study focuses on the problem of examining the role of various noise channels in the creation, dynamics, and decay of the entanglement during quantum operations, such as depolarizing, amplitude damping, and phase damping. The study is based on theoretical modeling and numerical simulations of multi-qubit quantum circuits to determine the stability of entangled states with respect to circuit depth and intensity of noise. Concurrence and von Neumann entropy are examples of entanglement measures that are used to characterize correlations between qubits as well as to trace the dynamics of these correlations across computational interactions. The results show that noise has major impacts on entanglement distribution, which tends to cause rapid decays in highly entangled states with increase in circuit complexity. The findings, however, also show that there are some circuit architectures and error-mitigation schemes that can somewhat sustain entanglement with moderate levels of noise. The paper also emphasizes the relevance of minimalizing sequence of gates, and reduced circuit depth in an effort to preserve useful entanglement in present-day quantum hardware. These observations help in understanding the behaviour of quantum correlations better in real world quantum devices and provide a way of developing more resilient quantum algorithms that would work on NISQ systems. In general, the article offers a systematic view on entanglement behavior in disordered quantum systems and highlights its value in the development of quantum computing applications in the near term.
We compute the dynamics of entanglement in the minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed boundary chaos. This consists of a free, non-interacting brickwork quantum circuit, in which chaos and ergodicity is induced by an impurity interaction, i.e., an entangling two-qudit gate, placed at the system’s boundary. We compute both the conventional bipartite entanglement entropy with respect to a connected subsystem including the impurity interaction for initial product states as well as the so-called operator entanglement entropy of initial local operators. Thereby we provide exact results in a particular scaling limit of both time and system size going to infinity for either very small or very large subsystems. We show that different classes of impurity interactions lead to very distinct entanglement dynamics. For impurity gates preserving a local product state forming the bulk of the initial state, entanglement entropies of states show persistent spikes with period set by the system size and suppressed entanglement in between, contrary to the expected linear growth in ergodic systems. We observe similar dynamics of operator entanglement for generic impurities. In contrast, for T-dual impurities, which remain unitary under partial transposition, we find entanglement entropies of both states and operators to grow linearly in time with the maximum possible speed allowed by the geometry of the system. The intensive nature of interactions in all cases causes entanglement to grow on extensive time scales proportional to system size.
Entanglement dynamics plays a crucial role in the development of scalable quantum information processing architectures. Quantum networks, composed of interconnected quantum nodes, offer promising avenues for the distribution and manipulation of quantum information over long distances. In this paper, we investigate the dynamics of entanglement in quantum networks and explore strategies for achieving scalable quantum information processing. the generation, distribution, and preservation of entanglement in various network topologies and investigate the impact of noise and decoherence on entanglement dynamics. Furthermore, we discuss potential applications of entanglement in quantum communication, cryptography, and computation, highlighting the importance of understanding and controlling entanglement dynamics for realizing practical quantum technologies. Through theoretical analysis and numerical simulations, we provide insights into the challenges and opportunities associated with entanglement dynamics in quantum networks, paving the way towards scalable quantum information processing architectures.