427 research outputs found

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    Towards Quantum Dynamics Simulation of Physical Systems: A Survey

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    After the emergence of quantum mechanics and realising its need for an accurate understanding of physical systems, numerical methods were being used to undergo quantum mechanical treatment. With increasing system correlations and size, numerical methods fell rather inefficient, and there was a need to simulate quantum mechanical phenomena on actual quantum computing hardware. Now, with noisy quantum computing machines that have been built and made available to use, realising quantum simulations are edging towards a practical reality. In this paper, we talk about the progress that has been made in the field of quantum simulations by actual quantum computing hardware and talk about some very fascinating fields where it has expanded its branches, too. Not only that, but we also review different software tool-sets available to date, which are to lay the foundation for realising quantum simulations in a much more comprehensive manner.Comment: 37 Pages with 13 Figures and 3 Table

    Laboratory directed research and development. FY 1995 progress report

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    Nonlinear Optics Quantum Computation and Quantum Simulation with Circuit-QED

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    Superconducting quantum circuits are a promising approach for realizations of large scale quantum information processing and quantum simulations. The Josephson junction, which forms the basis of superconducting circuits, is the only known nonlinear non-dissipative circuit element, and its inherent nonlinearities have found many different applications. In this thesis I discuss specific implementations of these circuits. I show that strong two-photon nonlinearities can be induced by coupling photons in the microwave domain to Josephson nonlinearities. I then propose a method to simulate a parent Hamiltonian that can potentially be used to observe fractional quantum Hall states of light. I will also explore how superconducting circuits can be used to modify system-bath couplings to emulate a chemical potential for photons. Finally, I consider the limitations of devising a scheme to couple superconducting circuits to trapped ions, and consider the challenges for such hybrid approaches

    Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

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    An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u

    Angles and devices for quantum approximate optimization

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    A potential application of emerging Noisy Intermediate-Scale Quantum (NISQ) devices is that of approximately solving combinatorial optimization problems. This thesis investigates a gate-based algorithm for this purpose, the Quantum Approximate Optimization Algorithm (QAOA), in two major themes. First, we examine how the QAOA resolves the problems it is designed to solve. We take a statistical view of the algorithm applied to ensembles of problems, first, considering a highly symmetric version of the algorithm, using Grover drivers. In this highly symmetric context, we find a simple dependence of the QAOA state’s expected value on how values of the cost function are distributed. Furthering this theme, we demonstrate that, generally, QAOA performance depends on problem statistics with respect to a metric induced by a chosen driver Hamiltonian. We obtain a method for evaluating QAOA performance on worst-case problems, those of random costs, for differing driver choices. Second, we investigate a QAOA context with device control occurring only via single-qubit gates, rather than using individually programmable one- and two-qubit gates. In this reduced control overhead scheme---the digital-analog scheme---the complexity of devices running QAOA circuits is decreased at the cost of errors which are shown to be non-harmful in certain regimes. We then explore hypothetical device designs one could use for this purpose.Eine mögliche Anwendung für “Noisy Intermediate-Scale Quantum devices” (NISQ devices) ist die näherungsweise Lösung von kombinatorischen Optimierungsproblemen. Die vorliegende Arbeit untersucht anhand zweier Hauptthemen einen gatterbasierten Algorithmus, den sogenannten “Quantum Approximate Optimization Algorithm” (QAOA). Zuerst prüfen wir, wie der QAOA jene Probleme löst, für die er entwickelt wurde. Wir betrachten den Algorithmus in einer Kombination mit hochsymmetrischen Grover-Treibern für statistische Ensembles von Probleminstanzen. In diesem Kontext finden wir eine einfache Abhängigkeit von der Verteilung der Kostenfunktionswerte. Weiterführend zeigen wir, dass die QAOA-Leistung generell von der Problemstatistik in Bezug auf eine durch den gewählten Treiber-Hamiltonian induzierte Metrik abhängt. Wir erhalten eine Methode zur Bewertung der QAOA-Leistung bei schwersten Problemen (solche zufälliger Kosten) für unterschiedliche Treiberauswahlen. Zweitens untersuchen wir eine QAOA-Variante, bei der sich die Hardware- Kontrolle nur auf Ein-Qubit-Gatter anstatt individuell programmierbare Ein- und Zwei-Qubit-Gatter erstreckt. In diesem reduzierten Kontrollaufwandsschema—dem digital-analogen Schema—sinkt die Komplexität der Hardware, welche die QAOASchaltungen ausführt, auf Kosten von Fehlern, die in bestimmten Bereichen als ungefährlich nachgewiesen werden. Danach erkunden wir hypothetische Hardware- Konzepte, die für diesen Zweck genutzt werden könnten

    Computational Intelligence and Complexity Measures for Chaotic Information Processing

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    This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value
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