124 research outputs found

    The Symmetry Method for Coloured Petri Nets

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    This booklet is the author's PhD-dissertation

    Gaussian Quantum Information

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    The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.Comment: 51 pages, 7 figures, submitted to Reviews of Modern Physic

    Exploring Quantum Computation Through the Lens of Classical Simulation

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    It is widely believed that quantum computation has the potential to offer an ex- ponential speedup over classical devices. However, there is currently no definitive proof of this separation in computational power. Such a separation would in turn imply that quantum circuits cannot be efficiently simulated classically. However, it is well known that certain classes of quantum computations nonetheless admit an efficient classical description. Recent work has also argued that efficient classical simulation of quantum circuits would imply the collapse of the Polynomial Hierarchy, something which is commonly invoked in clas- sical complexity theory as a no-go theorem. This suggests a route for studying this ‘quantum advantage’ through classical simulations. This project looks at the problem of classically simulating quantum circuits through decompositions into stabilizer circuits. These are a restricted class of quantum computation which can be efficiently simulated classically. In this picture, the rank of the decomposition determines the temporal and spatial complexity of the simulation. We approach the problem by considering classical simulations of stabilizer circuits, introducing two new representations with novel features compared to previous meth- ods. We then examine techniques for building these so-called ‘stabilizer rank’ decom- positions, both exact and approximate. Finally, we combine these two ingredients to introduce an improved method for classically simulating broad classes of circuits using the stabilizer rank method

    The Coherent Parity Check Framework for Quantum Error Correction

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    Quantum error correction protocols are an essential element in the design of any circuit-model quantum computer. In this thesis, I introduce the coherent parity check (CPC) framework for quantum error correction. CPC codes have a fundamental structure in which quantum parity check measurements are stored coherently and compared over time. The specific advantage of the CPC code structure is that it provides a way of creating new stabilizer codes from the starting point of any sequence of parity checks. I show that this freedom in the choice of parity checks can be used to derive methods for the construction of distance-three quantum codes based on almost any distance-three classical code. The CPC framework has further applications in machine search routines for code discovery, as well as in the design of bespoke codes tailored for the demands of a given device. Another feature of CPC codes is that they can be represented as factor graphs of the type commonly seen in classical error correction and machine learning. I outline a procedure for this mapping, and demonstrate how a quantum code can be derived by manipulating its factor graph representation. The aim of the factor graph mapping for CPC codes is to make it easier to adapt well-developed techniques from classical information theory for use with quantum codes. This will make the CPC framework a useful tool for the theoretical and practical study of quantum error correction codes as large-scale quantum computers move closer to becoming a reality

    Quantum dynamics in condensed phases : charge carrier mobility, decoherence, and excitation energy transfer

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2006.Vita.Includes bibliographical references.In this thesis, we develop analytical models for quantum systems and perform theoretical investigations on several dynamical processes in condensed phases. First, we study charge-carrier mobilities in organic molecular crystals, and develop a microscopic theory that describes both the coherent band-like and incoherent hopping transport observed in organic crystals. We investigate the structures of polaron states using a variational scheme, and calculate both band-like and hopping mobilities at a broad range of parameters. Our mobility calculations in 1-D nearest-neighbor systems predict universal band-like to hopping transitions, in agreement with experiments. Second, motivated by recent developments in quantum computing with solid-state systems, we propose an effective Hamiltonian approach to describe quantum dissipation and decoherence. We then applied this method to study the effect of noise in a number of quantum algorithms and calculate noise threshold for fault-tolerant quantum error corrections (QEC). In addition, we perform a systematic investigation on several variables that can affect the efficiency of the fault-tolerant QEC scheme, aiming to generate a generic picture on how to search for optimal circuit design for real physical implementations.(cont.) Third, we investigate the quantum coherence in the B800 ring of' of the purple bacterium Rps. acidophila and how it affects the dynamics of excitation energy transfer in a single LH2 complex. Our calculations suggest that the coherence in the B800 ring plays a significant role in both spectral and dynamical properties. Finally, we discussed the validity of Markovian master equations, and propose a concatenation scheme for applying Markovian master equations that absorbs the non-Markovian effects at short times in a natural manner. Applications of the concatenation scheme on the spin-boson problem show excellent agreements with the results obtained from the non-Markovian master equation at all parameter range studied.by Yuan-Chung Cheng.Ph.D

    Large-N Chern insulators: Lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect

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    Four-Fermi quantum field theories in (2+1) dimensions lie among the simplest models in high-energy physics, the understanding of which requires a non-perturbative lattice formulation addressing their strongly-coupled fixed points. These lattice models are also relevant in condensed matter, as they offer a neat playground to explore strong correlations in the quantum anomalous Hall (QAH) effect. We give a detailed description of our multidisciplinary approach to understand the fate of the QAH phases as the four-Fermi interactions are increased, which combines strong-coupling and effective-potential techniques, unveiling a rich phase diagram with large-NN Chern insulators and Lorentz-breaking fermion condensates. Moreover, this toolbox can be enlarged with recent advances in quantum information science, as we show that tensor-network algorithms based on projected entangled pairs can be used to improve our understanding of the strong-coupling limit. We also present a detailed scheme that uses ultra-cold atoms in optical lattices with synthetic spin-orbit coupling to build quantum simulators of these four-Fermi models. This yields a promising alternative to characterise the strongly-coupled fixed points and, moreover, could also explore real-time dynamics and finite-fermion densities

    Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches

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    Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries
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