[PDF] Characterisation And Optimality Of Open Quantum System Dynamics eBook

Author : Masoud Mohseni
Publisher :
Page : 496 pages
File Size : 11,3 MB
Release : 2007
Category :
ISBN : 9780494280799

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An optimal quantum algorithm for "direct characterization of quantum dynamics" (DCQD) is introduced. The DCQD method can be utilized to completely determine the quantum dynamical superoperator acting on an open quantum system. In contrast to all other known quantum process tomography (QPT) schemes, this scheme relies on error-detection techniques and does not require any quantum state tomography. By analysis of the number of required experimental configurations and quantum operations in a given Hilbert space, it is demonstrated that this approach is more efficient than all other known QPT schemes. DCQD can be applied, by construction, to the task of partial characterization of quantum dynamics. Specifically, it is demonstrated that the DCQD algorithm can be efficiently used for Hamiltonian identification, and also for simultaneous determination of both the relaxation time T1 and dephasing time T2. Furthermore, it is argued that the DCQD scheme is experimentally implementable in a variety of prominent quantum information processing systems, and it is explicitly shown how it can be physically realized in photonic systems with present day technology. The ability of a quantum system to perform arbitrary or "universal" quantum operations is restricted to its naturally available/controllable interactions. It is shown that quantum systems with an effective exchange interaction can be made operationally universal by utilizing a subspace or a subsystem of the combined principal system and an auxiliary system. Moreover, it is demonstrated that universal fault-tolerant quantum computation can be performed on these systems without utilizing any form of single-qubit control. Characterization and control of open quantum systems are among the central and fundamental problems in quantum physics. A crucial primitive is the characterization of the dynamics of a quantum system that has an unknown interaction with its embedding environment. Another essential task is to control the decoherence of an open quantum system by using naturally available interactions. This thesis addresses the above fundamental problems in two separate parts. In the first part, a general theory for direct and complete characterization of quantum dynamics is introduced. In the second part, a scheme for performing arbitrary quantum operations on spin-based quantum systems is presented. This scheme can be implemented in the presence of environmental noise and faulty quantum operations without need to control the state of spins individually.

Author : Cecilia Carolina López
Publisher :
Page : 162 pages
File Size : 40,21 MB
Release : 2009
Category :
ISBN :

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One of the biggest challenges in the physical realization of quantum information processing (QIP) is the precise control of the system. In order to achieve this, we characterize the gates, errors, and noise occurring in experimental setups. In this thesis we develop and further study characterization methods, putting particular emphasis on the scalability problem: O(D4) parameters describe the dynamics of an open quantum system of dimension D, thus O(D4) resources are in principle required to characterize it -- which is a problem in QIP where the desired systems are large (D = 2n for n qubits). We first study the fidelity decay (also called Loschmidt echo) of the system, for many steps under the progressive randomization due to a one-qubit twirl. We show how this quantity encodes useful information about the process begin twirled. We then present a method to measure the magnitude of the multi-body correlations that scales as O(nw), when only up to w-body interactions are expected among the n qubits. We implemented this method in a four-qubit liquid-state Nuclear Magnetic Resonance (NMR) QIP device, demonstrating its potential and feasibility. The experimental work also pointed out the need for robust procedures and the role of implementation errors, while deepening our knowledge of NMR QIP dynamics. We also report on several practical aspects of the experiment, including details on twirls using random rotations and Clifford operators. We furthermore relate this work to recent developments in the community, arriving to a more comprehensive protocol and establishing an intrinsic hierarchy of characterization algorithms. Finally, we study the many-step fidelity decay when using a flawed twirl, thus acknowledging the most realistic scenario where we have a faulty device attempting to characterize itself. Our preliminary work points towards the use of a many-step scheme that promises robust scalable tools to characterize the twirl operators themselves.

Author : Stéphane Attal
Publisher : Springer
Page : 347 pages
File Size : 12,55 MB
Release : 2006-08-18
Category : Mathematics
ISBN : 3540339221

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Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

Author : Heinz-Peter Breuer
Publisher : Oxford University Press, USA
Page : 648 pages
File Size : 14,19 MB
Release : 2002
Category : Mathematics
ISBN : 9780198520634

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This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

Author : Manuel Gessner
Publisher : Springer
Page : 357 pages
File Size : 40,66 MB
Release : 2016-10-03
Category : Science
ISBN : 331944459X

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This thesis sheds new light on the fascinating properties of composite quantum systems. Quantum systems of different sizes, ranging from small bipartite systems to large many-body ensembles, can be studied with the help of modern quantum optical experiments. These experiments make it possible to observe a broad variety of striking features, including nonclassical correlations, complex dynamics and quantum phase transitions. By adopting the complementary perspectives of quantum information theory, quantum chemistry and many-body theory, the thesis develops new methods for the efficient characterization and description of interacting, composite quantum systems.

Author : Stéphane Attal
Publisher : Springer
Page : 326 pages
File Size : 42,27 MB
Release : 2006-08-18
Category : Mathematics
ISBN : 3540339671

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This volume is the third and last of a series devoted to the lecture notes of the Grenoble Summer School on “Open Quantum Systems” which took place at the th th Institut Fourier from June 16 to July 4 2003. The contributions presented in this volumecorrespondtoexpanded versionsofthelecturenotesprovidedbytheauthors to the students of the Summer School. The corresponding lectures were scheduled in the last part of the School devoted to recent developments in the study of Open Quantum Systems. Whereas the rst two volumes were dedicated to a detailed exposition of the mathematical techniques and physical concepts relevant in the study of Open S- tems with noapriori pre-requisites, the contributions presented in this volume request from the reader some familiarity with these aspects. Indeed, the material presented here aims at leading the reader already acquainted with the basics in ? quantum statistical mechanics, spectral theory of linear operators,C -dynamical systems, and quantum stochastic differential equations to the front of the current research done on various aspects of Open Quantum Systems. Nevertheless, pe- gogical efforts have been made by the various authors of these notes so that this volume should be essentially self-contained for a reader with minimal previous - posure to the themes listed above. In any case, the reader in need of complements can always turn to these rst two volumes. The topics covered in these lectures notes start with an introduction to n- equilibrium quantum statistical mechanics.