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

Complex Quantum Networks: a Topical Review

These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.Comment: 103 pages + 29 pages of references, 26 figure

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