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Science Technology and Engineer

Using Open Quantum System Theory to Study Quantum Information

BI Qia

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Based on the subdynamical kinetic equation describing the openquantum system, the general method to deal with the decoherence-free for thequantum computing, multiqubit computing and error-avoiding codes in thesubspace using quantum dots are briefly discussed.

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Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. Scalable quantum computers require a far-reaching theory of fault-tolerant quantum computation. This comprehensive text, written by leading experts in the field, focuses on quantum error correction and thoroughly covers the theory as well as experimental and practical issues. The book is not limited to a single approach, but reviews many different methods to control quantum errors, including topological codes, dynamical decoupling and decoherence-free subspaces. Basic subjects as well as advanced theory and a survey of topics from cutting-edge research make this book invaluable both as a pedagogical introduction at the graduate level and as a reference for experts in quantum information science.
An approach is presented for directly constructing cn-Not multi-qubit logic gates using quantum dots. In addition, error-avoiding codes in the projected subspace are discussed, offering a potentially robust scheme for protecting against decoherence. The following general conditions were found: (1) a projected subspace can always be constructed, in which decoherence effects can be cancelled by adjusting the interaction coupling time, enabling error-correction to be performed. This subspace is closed for the projected states. (2) The necessary and sufficient conditions for a decoherence-free subspace are that the second term in the subdynamic equation, be equal to zero. Commonly formulated conditions for a decoherence-free subspace are shown to be particular approximations of this condition, including the so-called Born–Markovian approximation.
Quantum physics is the cornerstone of contemporary science,and has led to a revolution in high-tech development. Its combination with information science has resulted in the interdisciplinary field of quantum information. It provides a new train of thought for overcoming the limits of computer chip size. Since 1987,our investigations on quantum open system theory,quantum ecoherence,and the fundamental problems of quantum physics have kept pace with the rapid development of quantum information science in the last decade. Starting with Huan-Wu Peng's important research on open quantum systems (the quantum damped harmonic oscillator) at the end of the 1970s,we will review the basic concepts and scientific importance of this field. At the same time,we will give a brief description of our series of studies on the theory of quantum open systems and its applications in quantum information.
Open quantum systems describe quantum systems that interact unavoidably with their environments. These notes introduce the physical origins of decoherence and dissipation in realistic settings, developing the theoretical framework of reduced dynamics and quantum master equations within the connection to thermodynamics in the quantum regime. Additionally, a set of relevant exercises are proposed to reinforce the acquisition of knowledge. The text equips readers with the tools to model and analyze open quantum dynamics.
A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1.1.1. This permits a universal formalism to be presented---the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two-qubit computing system. A general criteria for constructing a DF-projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is general and appears to be applicable to any type of decoherence.
Accurate models for open quantum systems─quantum states that have nontrivial interactions with their environment─may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction of static and dynamic molecular properties. In recent years, quantum algorithms have been leveraged for the computation of open quantum systems as the predicted quantum advantage of quantum devices over classical ones may allow previously inaccessible applications. Accomplishing this goal will require input and expertise from different research perspectives, as well as the training of a diverse quantum workforce, making a compilation of current quantum methods for treating open quantum systems both useful and timely. In this Review, we first provide a succinct summary of the fundamental theory of open quantum systems and then delve into a discussion on recent quantum algorithms. We conclude with a discussion of pertinent applications, demonstrating the applicability of this field to realistic chemical, biological, and material systems.