Quantum complex networks

This Thesis focuses on networks of interacting quantum harmonic oscillators and in particular, on them as environments for an open quantum system, their probing via the open system, their transport properties, and their experimental implementation. Exact Gaussian dynamics of such networks is considered throughout the Thesis. Networks of interacting quantum systems have been used to model structured environments before, but most studies have considered either small or non-complex networks. Here this problem is addressed by investigating what kind of environments complex networks of quantum systems are, with specific attention paid on the presence or absence of memory effects (non-Markovianity) of the reduced open system dynamics. The probing of complex networks is considered in two different scenarios: when the probe can be coupled to any system in the network, and when it can be coupled to just one. It is shown that for identical oscillators and uniform interaction strengths between them, much can be said about the network also in the latter case. The problem of discriminating between two networks is also discussed. While state transfer between two sites in a (typically non-complex) network is a well-known problem, this Thesis considers a more general setting where multiple parties send and receive quantum information simultaneously through a quantum network. It is discussed what properties would make a network suited for efficient routing, and what is needed for a systematic search and ranking of such networks. Finding such networks complex enough to be resilient to random node or link failures would be ideal. The merit and applicability of the work described so far depends crucially on the ability to implement networks of both reasonable size and complex structure, which is something the previous proposals lack. The ability to implement several different networks with a fixed experimental setup is also highly desirable. In this Thesis the problem is solved with a proposal of a fully reconfigurable experimental realization, based on mapping the network dynamics to a multimode optical platform

Universal Quantum Cloning

After introducing the no-cloning theorem and the most common forms of approximate quantum cloning, universal quantum cloning is considered in detail. The connections it has with universal NOT-gate, quantum cryptography and state estimation are presented and briefly discussed. The state estimation connection is used to show that the amount of extractable classical information and total Bloch vector length are conserved in universal quantum cloning. The 1 2 qubit cloner is also shown to obey a complementarity relation between local and nonlocal information. These are interpreted to be a consequence of the conservation of total information in cloning. Finally, the performance of the 1 M cloning network discovered by Bužek, Hillery and Knight is studied in the presence of decoherence using the Barenco et al. approach where random phase fluctuations are attached to 2-qubit gates. The expression for average fidelity is calculated for three cases and it is found to depend on the optimal fidelity and the average of the phase fluctuations in a specific way. It is conjectured to be the form of the average fidelity in the general case. While the cloning network is found to be rather robust, it is nevertheless argued that the scalability of the quantum network implementation is poor by studying the effect of decoherence during the preparation of the initial state of the cloning machine in the 1 ! 2 case and observing that the loss in average fidelity can be large. This affirms the result by Maruyama and Knight, who reached the same conclusion in a slightly different manner.Siirretty Doriast

Complex quantum networks as structured environments: engineering and probing

We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity.Comment: 7 pages, 4 figures. v3: update to match published versio

Gaussian states provide universal and versatile quantum reservoir computing

We establish the potential of continuous-variable Gaussian states in performing reservoir computing with linear dynamical systems in classical and quantum regimes. Reservoir computing is a machine learning approach to time series processing. It exploits the computational power, high-dimensional state space and memory of generic complex systems to achieve its goal, giving it considerable engineering freedom compared to conventional computing or recurrent neural networks. We prove that universal reservoir computing can be achieved without nonlinear terms in the Hamiltonian or non-Gaussian resources. We find that encoding the input time series into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that reservoir computing can in principle be powered by quantum fluctuations, such as squeezed vacuum, instead of classical intense fields. Our results introduce a new research paradigm for quantum reservoir computing and the engineering of Gaussian quantum states, pushing both fields into a new direction.Comment: 13 pages, 4 figure

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

Quantum reservoir computing (QRC) and quantum extreme learning machines (QELM) are two emerging approaches that have demonstrated their potential both in classical and quantum machine learning tasks. They exploit the quantumness of physical systems combined with an easy training strategy, achieving an excellent performance. The increasing interest in these unconventional computing approaches is fueled by the availability of diverse quantum platforms suitable for implementation and the theoretical progresses in the study of complex quantum systems. In this review article, recent proposals and first experiments displaying a broad range of possibilities are reviewed when quantum inputs, quantum physical substrates and quantum tasks are considered. The main focus is the performance of these approaches, on the advantages with respect to classical counterparts and opportunities

Analytical Evidence of Nonlinearity in Qubits and Continuous-Variable Quantum Reservoir Computing

The natural dynamics of complex networks can be harnessed for information processing purposes. A paradigmatic example are artificial neural networks used for machine learning. In this context, quantum reservoir computing (QRC) constitutes a natural extension of the use of classical recurrent neural networks using quantum resources for temporal information processing. Here, we explore the fundamental properties of QRC systems based on qubits and continuous variables. We provide analytical results that illustrate how nonlinearity enters the input–output map in these QRC implementations. We find that the input encoding through state initialization can serve to control the type of nonlinearity as well as the dependence on the history of the input sequences to be processed.</p

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

Quantum reservoir computing and quantum extreme learning machines are two emerging approaches that have demonstrated their potential both in classical and quantum machine learning tasks. They exploit the quantumness of physical systems combined with an easy training strategy, achieving an excellent performance. The increasing interest in these unconventional computing approaches is fueled by the availability of diverse quantum platforms suitable for implementation and the theoretical progresses in the study of complex quantum systems. In this review article, recent proposals and first experiments displaying a broad range of possibilities are reviewed when quantum inputs, quantum physical substrates and quantum tasks are considered. The main focus is the performance of these approaches, on the advantages with respect to classical counterparts and opportunities

Gaussian states are enough for universal and powerful quantum reservoir computing

Trabajo presentado en el 2nd International Workshop on Quantum Network Science (NetSci 2020 Satellite Workshop), celebrado el 18 de spetiembre de 2020.Machine learning tasks where one time series needs to be transformed to another include chaotic time series prediction, restoring a signal transformed by transmission via a noisy channel and approximating a nonlinear function of a time series. The central idea of reservoir computing is to drive a dynamical system with the input time series and train a simple readout mechanism that maps the system observables to desired output. If the observables are (non)linear functions of input, we say there is (non)linear memory. For rich enough dynamics acting as a source of memory, nontrivial information processing can be realized even by a linear function of reservoir observables. This leads to simple and fast training, a major advantage over alternative machine learning solutions. In the past few years proposals have been made to harness the dynamics of quantum many-body systems for reservoir computing. We establish the potential of continuous-variable Gaussian states in performing reservoir computing with linear systems. The model consists of a network of interacting quantum harmonic oscillators where the state of a subset of oscillators is periodically reset according to input, while the output is taken to be a trained function of the observables of the rest of the network, playing the role of the reservoir. We show that encoding the classical input into quantum states acts as both a source and means to control nonlinear memory, even when the readout is linear in reservoir observables. Another source of nonlinear memory is provided by correlations in reservoir observables. We verify that this is enough to succeed in many typical reservoir computing tasks while keeping the readout linear. We furthermore show that thanks to certain properties of the reservoir memory, letting the readout be polynomial in reservoir observables makes even universal time series processing, i.e. universal reservoir computing, possible both in classical and quantum regime. In stark contrast with quantum computing with continuous-variable systems where it is well-known that Gaussian resources are not enough for universality, our results show that universal reservoir computing does not require non-Gaussian resources or nonlinearity in the Hamiltonian, increasing its feasibility in state-of-the-art optical platforms